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Nth Term of Arithmetic Progression given Pth and Qth Terms Formula

GoNth Term of Arithmetic Progression Formula

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The Nth Term of Progression is the term corresponding to the index or position n from the beginning in the given Progression. Check FAQs

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})

T_n - Nth Term of Progression?T_p - Pth Term of Progression?q - Index Q of Progression?T_q - Qth Term of Progression?p - Index P of Progression?n - Index N of Progression?

Nth Term of Arithmetic Progression given Pth and Qth Terms Example

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Here is how the Nth Term of Arithmetic Progression given Pth and Qth Terms equation looks like with Values.

Here is how the Nth Term of Arithmetic Progression given Pth and Qth Terms equation looks like with Units.

Here is how the Nth Term of Arithmetic Progression given Pth and Qth Terms equation looks like.

60 = (\frac{50 \cdot (8 - 1) - 80 \cdot (5 - 1)}{8 - 5}) + (6 - 1) \cdot (\frac{80 - 50}{8 - 5})

60 = (\frac{50 \cdot (8 - 1) - 80 \cdot (5 - 1)}{8 - 5}) + (6 - 1) \cdot (\frac{80 - 50}{8 - 5})

60 = (\frac{50 \cdot (8 - 1) - 80 \cdot (5 - 1)}{8 - 5}) + (6 - 1) \cdot (\frac{80 - 50}{8 - 5})

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Nth Term of Arithmetic Progression given Pth and Qth Terms Solution

Follow our step by step solution on how to calculate Nth Term of Arithmetic Progression given Pth and Qth Terms?

FIRST Step Consider the formula

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})

Next Step Substitute values of Variables

∴

T n = (\frac{50 \cdot (8 - 1) - 80 \cdot (5 - 1)}{8 - 5}) + (6 - 1) \cdot (\frac{80 - 50}{8 - 5})

Next Step Prepare to Evaluate

∴

T n = (\frac{50 \cdot (8 - 1) - 80 \cdot (5 - 1)}{8 - 5}) + (6 - 1) \cdot (\frac{80 - 50}{8 - 5})

LAST Step Evaluate

∴

T n = 60

Nth Term of Arithmetic Progression given Pth and Qth Terms Formula Elements

Variables

Nth Term of Progression

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

Symbol: T_n

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Nth Term of Progression

Pth Term of Progression

The Pth Term of Progression is the term corresponding to the index or position p from the beginning of the given Progression.

Symbol: T_p

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Pth Term of Progression

Index Q of Progression

The Index Q of Progression is the value of q for the qth term or the position of the qth term in the Progression.

Symbol: q

Measurement: NAUnit: Unitless

Note: Value should be greater than 1.

Formulas to find Index Q of Progression

Qth Term of Progression

The Qth Term of Progression is the term corresponding to the index or position q from the beginning of the given Progression.

Symbol: T_q

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Qth Term of Progression

Index P of Progression

The Index P of Progression is the value of p for the pth term or the position of the pth term in the Progression.

Symbol: p

Measurement: NAUnit: Unitless

Note: Value should be greater than 1.

Formulas to find Index P of Progression

Index N of Progression

The Index N of Progression is the value of n for the nth term or the position of the nth term in a Progression.

Symbol: n

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Index N of Progression

Other Formulas to find Nth Term of Progression

Go Nth Term of Arithmetic Progression

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

Other formulas in Nth Term of Arithmetic Progression category

Go Common Difference of Arithmetic Progression

d = T n - T n-1

Go Sum of First N Terms of Arithmetic Progression

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

Go Sum of Total Terms of Arithmetic Progression given Last Term

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

Go Common Difference of Arithmetic Progression given Last Term

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

How to Evaluate Nth Term of Arithmetic Progression given Pth and Qth Terms?

Nth Term of Arithmetic Progression given Pth and Qth Terms evaluator uses Nth Term of Progression = ((Pth Term of Progression*(Index Q of Progression-1)-Qth Term of Progression*(Index P of Progression-1))/(Index Q of Progression-Index P of Progression))+(Index N of Progression-1)*((Qth Term of Progression-Pth Term of Progression)/(Index Q of Progression-Index P of Progression)) to evaluate the Nth Term of Progression, 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. Nth Term of Progression is denoted by T_n symbol.

How to evaluate Nth Term of Arithmetic Progression given Pth and Qth Terms using this online evaluator? To use this online evaluator for Nth Term of Arithmetic Progression given Pth and Qth Terms, enter Pth Term of Progression (T_p), Index Q of Progression (q), Qth Term of Progression (T_q), Index P of Progression (p) & Index N of Progression (n) and hit the calculate button.

FAQs on Nth Term of Arithmetic Progression given Pth and Qth Terms

What is the formula to find Nth Term of Arithmetic Progression given Pth and Qth Terms?

The formula of Nth Term of Arithmetic Progression given Pth and Qth Terms is expressed as Nth Term of Progression = ((Pth Term of Progression*(Index Q of Progression-1)-Qth Term of Progression*(Index P of Progression-1))/(Index Q of Progression-Index P of Progression))+(Index N of Progression-1)*((Qth Term of Progression-Pth Term of Progression)/(Index Q of Progression-Index P of Progression)). Here is an example- 39 = ((50*(8-1)-80*(5-1))/(8-5))+(6-1)*((80-50)/(8-5)).

How to calculate Nth Term of Arithmetic Progression given Pth and Qth Terms?

With Pth Term of Progression (T_p), Index Q of Progression (q), Qth Term of Progression (T_q), Index P of Progression (p) & Index N of Progression (n) we can find Nth Term of Arithmetic Progression given Pth and Qth Terms using the formula - Nth Term of Progression = ((Pth Term of Progression*(Index Q of Progression-1)-Qth Term of Progression*(Index P of Progression-1))/(Index Q of Progression-Index P of Progression))+(Index N of Progression-1)*((Qth Term of Progression-Pth Term of Progression)/(Index Q of Progression-Index P of Progression)).

What are the other ways to Calculate Nth Term of Progression?

Here are the different ways to Calculate Nth Term of Progression-

Nth Term of Progression=First Term of Progression+(Index N of Progression-1)*Common Difference of Progression

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Nth Term of Arithmetic Progression given Pth and Qth Terms Formula

​GoNth Term of Arithmetic Progression Formula

Nth Term of Arithmetic Progression given Pth and Qth Terms Example

Nth Term of Arithmetic Progression given Pth and Qth Terms Solution

Nth Term of Arithmetic Progression given Pth and Qth Terms Formula Elements

Other Formulas to find Nth Term of Progression

Other formulas in Nth Term of Arithmetic Progression category

How to Evaluate Nth Term of Arithmetic Progression given Pth and Qth Terms?

FAQs on Nth Term of Arithmetic Progression given Pth and Qth Terms

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GoNth Term of Arithmetic Progression Formula