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Nth Term of Arithmetic Progression

The Nth Term of Arithmetic Progression formula is defined as the term corresponding to the index or position n from the beginning in the given Arithmetic Progression.

T n = a + (n - 1) \cdot d

Last Term of Arithmetic Progression

The Last Term of Arithmetic Progression formula is defined as term at which the given Arithmetic Progression terminates.

l = a + ((n Total - 1) \cdot d)

First Term of Arithmetic Progression

The First Term of Arithmetic Progression formula is defined as the term at which the given Arithmetic Progression starts.

a = T n - ((n - 1) \cdot d)

Number of Terms of Arithmetic Progression

The Number of Terms of Arithmetic Progression formula is defined as the value of n for the nth term or the position of the nth term in an Arithmetic Progression.

n = (\frac{T n - a}{d}) + 1

Nth Term from End of Arithmetic Progression

The Nth Term from End of Arithmetic Progression formula is defined as the term corresponding to the index or position n starting from the end of the given Arithmetic Progression.

T n(End) = a + (n Total - n) \cdot d

Common Difference of Arithmetic Progression

The Common Difference of Arithmetic Progression formula is defined as the difference between two consecutive terms of an Arithmetic Progression, which is always a constant.

d = T n - T n-1

Sum of Total Terms of Arithmetic Progression

The Sum of Total Terms of Arithmetic Progression formula is defined as the summation of the terms starting from the first to the last term of given Arithmetic Progression.

S Total = (\frac{n Total}{2}) \cdot ((2 \cdot a) + ((n Total - 1) \cdot d))

Sum of Last N Terms of Arithmetic Progression

The Sum of Last N Terms of Arithmetic Progression formula is defined as the summation of the terms starting from the end to the nth term of given Arithmetic Progression.

S n(End) = (\frac{n}{2}) \cdot ((2 \cdot a) + (d \cdot ((2 \cdot n Total) - n - 1)))

Sum of First N Terms of Arithmetic Progression

The Sum of First N Terms of Arithmetic Progression formula is defined as the summation of the terms starting from the first to the nth term of given Arithmetic Progression.

S n = (\frac{n}{2}) \cdot ((2 \cdot a) + ((n - 1) \cdot d))

Number of Total Terms of Arithmetic Progression

The Number of Total Terms of Arithmetic Progression formula is defined as the total number of terms present in the given sequence of Arithmetic Progression.

n Total = (\frac{l - a}{d}) + 1

Nth Term of Arithmetic Progression given Last Term

The Nth Term of Arithmetic Progression given Last Term formula is defined as the term corresponding to the index or position n from the beginning in the given Arithmetic Progression, calculated using the last term of the Arithmetic Progression.

T n = a + (n - 1) \cdot (\frac{l - a}{n Total - 1})

Last Term of Arithmetic Progression given Nth Term

The Last Term of Arithmetic Progression given Nth Term formula is defined as the term at which the given Arithmetic Progression terminates and calculated using the nth term of the Arithmetic Progression.

l = a + (n Total - 1) \cdot (\frac{T n - a}{n - 1})

First Term of Arithmetic Progression given Last Term

The First Term of Arithmetic Progression given Last Term formula is defined as the term at which the given Arithmetic Progression starts, calculated using the last term of the Arithmetic Progression.

a = l - ((n Total - 1) \cdot d)

Nth Term of Arithmetic Progression given Pth and Qth Terms

The Nth Term of Arithmetic Progression given Pth and Qth Terms formula is defined as the term corresponding to the index or position n from the beginning in the given Arithmetic Progression, and calculated using the pth and qth terms of the Arithmetic Progression.

T n = (\frac{T p \cdot (q - 1) - T q \cdot (p - 1)}{q - p}) + (n - 1) \cdot (\frac{T q - T p}{q - p})

Common Difference of Arithmetic Progression given Nth Term

The Common Difference of Arithmetic Progression given Nth Term formula is defined as the difference between two consecutive terms of an Arithmetic Progression, which is always a constant and calculated using the nth term of Arithmetic Progression.

d = \frac{T n - a}{n - 1}

Common Difference of Arithmetic Progression given Last Term

The Common Difference of Arithmetic Progression given Last Term formula is defined as the difference between two consecutive terms of an Arithmetic Progression, which is always a constant, and calculated using the first term, last term and the number of terms in an Arithmetic Progression.

d = (\frac{l - a}{n Total - 1})

Nth Term from End of Arithmetic Progression given Last Term

The Nth Term from End of Arithmetic Progression given Last Term formula is defined as the term corresponding to the index or position n starting from the end of the given Arithmetic Progression, calculated using the last term of the Arithmetic Progression.

T n(End) = l - (n - 1) \cdot d

Last Term of Arithmetic Progression given Pth and Qth Terms

The Last Term of Arithmetic Progression given Pth and Qth Terms formula is defined as the term at which the given Arithmetic Progression terminates and calculated using the pth and qth terms of the Arithmetic Progression.

l = (\frac{T p \cdot (q - 1) - T q \cdot (p - 1)}{q - p}) + (n Total - 1) \cdot (\frac{T q - T p}{q - p})

Last Term of Arithmetic Progression given Sum of Total Terms

The Last Term of Arithmetic Progression given Sum of Total Terms formula is defined as the term at which the given Arithmetic Progression terminates and calculated using the sum of total terms of given Arithmetic Progression.

l = (\frac{2 \cdot S Total}{n Total}) - a

Sum of First N Terms of Arithmetic Progression given NthTerm

The Sum of First N Terms of Arithmetic Progression given NthTerm formula is defined as the summation of the terms starting from the first to the nth term of given Arithmetic Progression, and is calculated using the nth term of the given Arithmetic Progression.

S n = (\frac{n}{2}) \cdot (a + T n)

Sum of Total Terms of Arithmetic Progression given Last Term

The Sum of Total Terms of Arithmetic Progression given Last Term formula is defined as the summation of the terms starting from the first to the last term of given Arithmetic Progression, and is calculated using the last term of the given Arithmetic Progression.

S Total = (\frac{n Total}{2}) \cdot (a + l)

First Term of Arithmetic Progression given Pth and Qth Terms

The First Term of Arithmetic Progression given Pth and Qth Terms formula is defined as the term at which the given Arithmetic Progression starts, and calculated using the pth and qth terms of Arithmetic Progression.

a = \frac{T p \cdot (q - 1) - T q \cdot (p - 1)}{q - p}

Sum of Terms from Pth to Qth Terms of Arithmetic Progression

Sum of Terms from Pth to Qth Terms of Arithmetic Progression formula is defined as the summation of the terms starting from the pth term to the qth term of given Arithmetic Progression.

S p-q = (\frac{q - p + 1}{2}) \cdot ((2 \cdot a) + ((p + q - 2) \cdot d))

Sum of Last N Terms of Arithmetic Progression given Last Term

The Sum of Last N Terms of Arithmetic Progression given Last Term formula is defined as the summation of the terms starting from the end to the nth term of given Arithmetic Progression, and calculated using last term of Arithmetic Progression.

S n(End) = (\frac{n}{2}) \cdot ((2 \cdot l) + (d \cdot (1 - n)))

Last Term of Arithmetic Progression given Sum of Last N Terms

The Last Term of Arithmetic Progression given Sum of Last N Terms formula is defined as the term at which the given Arithmetic Progression terminates and calculated using the sum of the last n terms of the Arithmetic Progression.

l = (\frac{S n(End)}{n} - \frac{d \cdot (1 - n)}{2})

Nth Term of Arithmetic Progression given Sum of First N Terms

The Nth Term of Arithmetic Progression given Sum of First N Terms formula is defined the term corresponding to the index or position n from the beginning in the given Arithmetic Progression, and calculated using the sum of first n terms of given Arithmetic Progression.

T n = (\frac{2 \cdot S n}{n}) - a

Common Difference of Arithmetic Progression given Pth and Qth Terms

The Common Difference of Arithmetic Progression given Pth and Qth Terms formula is defined as the difference between two consecutive terms of an Arithmetic Progression, which is always a constant, and calculated using the pth and the qth terms of an Arithmetic Progression.

d = (\frac{T q - T p}{q - p})

Number of Terms of Arithmetic Progression given Sum of First N Terms

The Number of Terms of Arithmetic Progression given Sum of First N Terms formula is defined as the value of n for the nth term or the position of the nth term in an Arithmetic Progression, and calculated using the sum of first n terms of given Arithmetic Progression.

n = (\frac{2 \cdot S n}{a + T n})

Sum of Last N Terms of Arithmetic Progression given Nth Term from End

The Sum of Last N Terms of Arithmetic Progression given Nth Term from End formula is defined as the summation of the terms starting from the end to the nth term of given Arithmetic Progression, and calculated using the nth term from end of Arithmetic Progression.

S n(End) = (\frac{n}{2}) \cdot (l + T n(End))

Number of Total Terms of Arithmetic Progression given Sum of Total Terms

The Number of Total Terms of Arithmetic Progression given Sum of Total Terms formula is defined as the total number of terms present in the given sequence of Arithmetic Progression, and calculated using sum of total terms, first term and last term Arithmetic Progression.

n Total = (\frac{2 \cdot S Total}{a + l})

Nth Term of Arithmetic Geometric Progression

The Nth Term of Arithmetic Geometric Progression formula defined as the term corresponding to the index or position n from the beginning in the given Arithmetic Geometric Progression.

T n = (a + ((n - 1) \cdot d)) \cdot (r^{n - 1})

Sum of Infinite Arithmetic Geometric Progression

The Sum of Infinite Arithmetic Geometric Progression is the summation of the terms starting from the first term to the infinite term of given Arithmetic Geometric Progression.

S ∞ = (\frac{a}{1 - r ∞}) + (\frac{d \cdot r ∞}{{(1 - r ∞)}^{2}})

Sum of First N Terms of Arithmetic Geometric Progression

The Sum of First N Terms of Arithmetic Geometric Progression formula is defined as the summation of the terms starting from the first to the nth term of given Arithmetic Geometric Progression.

S n = (\frac{a - ((a + (n - 1) \cdot d) \cdot r^{n})}{1 - r}) + (d \cdot r \cdot \frac{1 - r^{n - 1}}{{(1 - r)}^{2}})

Arithmetic Mean of N Numbers

The Arithmetic Mean of N Numbers formula is defined as the average value or mean which signifies the central tendency of the set of n numbers by finding the sum of their values.

AM = \frac{S Arithmetic}{n}

Arithmetic Mean of Two Numbers

Arithmetic Mean of Two Numbers formula is defined as the average value or mean which signifies the central tendency of the set of two numbers by finding the sum of their values.

AM = \frac{n 1 + n 2}{2}

Arithmetic Mean of Four Numbers

Arithmetic Mean of Four Numbers formula is defined as the average value or mean which signifies the central tendency of the set of four numbers by finding the sum of their values.

AM = \frac{n 1 + n 2 + n 3 + n 4}{4}

Arithmetic Mean of Three Numbers

The Arithmetic Mean of Three Numbers formula is defined as the average value or mean which signifies the central tendency of the set of three numbers by finding the sum of their values.

AM = \frac{n 1 + n 2 + n 3}{3}

Nth Term of Harmonic Progression

The Nth Term of Harmonic Progression formula is defined as the term corresponding to the index or position n from the beginning in the given Harmonic Progression.

T n = \frac{1}{a + (n - 1) \cdot d}

Nth Term of Geometric Progression

The Nth Term of Geometric Progression formula is defined as the term corresponding to the index or position n from the beginning of the given Geometric Progression.

T n = a \cdot (r^{n - 1})

Last Term of Geometric Progression

The Last Term of Geometric Progression formula is defined as the term at which the given Geometric Progression terminates.

l = a \cdot r^{n Total - 1}

First Term of Harmonic Progression

The First Term of Harmonic Progression formula is defined as the reciprocal of the first term of the given Harmonic Progression, which is the first term of the corresponding Arithmetic Progression.

a = \frac{1}{T n} - ((n - 1) \cdot d)

First Term of Geometric Progression

The First Term of Geometric Progression formula is defined as the term at which the given Geometric Progression starts.

a = \frac{T n}{r^{n - 1}}

Sum of Infinite Geometric Progression

The Sum of Infinite Geometric Progression formula is defined as the summation of the terms starting from the first term to the infinite term of given Infinite Geometric Progression.

S ∞ = \frac{a}{1 - r ∞}

Common Ratio of Geometric Progression

The Common Ratio of Geometric Progression formula is defined as the ratio of any term in the Geometric Progression to its preceding term.

r = \frac{T n}{T n-1}

Number of Terms of Harmonic Progression

The Number of Terms of Harmonic Progression formula is defined as the total number of terms present in the given sequence of Harmonic Progression.

n = (\frac{\frac{1}{T n} - a}{d}) + 1

Number of Terms of Geometric Progression

The Number of Terms of Geometric Progression formula is defined as the value of n for the nth term or the position of the nth term in a Geometric Progression.

n = \log (r, \frac{T n}{a}) + 1

Common Difference of Harmonic Progression

The Common Difference of Harmonic Progression formula is defined as the difference of reciprocal of an arbitrary term from the reciprocal of its proceeding term of the Harmonic Progression, which is the common difference of the corresponding Arithmetic Progression.

d = (\frac{1}{T n} - \frac{1}{T n-1})

Nth Term of Harmonic Progression from End

The Nth Term of Harmonic Progression from End formula is defined as the term corresponding to the index or position n from the end of the given Harmonic Progression.

T n = \frac{1}{l - (n - 1) \cdot d}

Arithmetic Mean of First N Natural Numbers

The Arithmetic Mean of First N Natural Numbers formula is defined as the average value or mean which signifies the central tendency of the first n natural numbers by finding the sum of their values.

AM = \frac{n + 1}{2}

Nth Term from End of Geometric Progression

The Nth Term from End of Geometric Progression formula is defined as the term corresponding to the index or position n starting from the end of the given Geometric Progression.

T n(End) = a \cdot (r^{n Total - n})

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