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Nth Term of Arithmetic Progression given Sum of First N Terms Formula

GoNth Term of Arithmetic Progression Formula

GoNth Term of Arithmetic Progression given Pth and Qth Terms 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{2 \cdot S n}{n}) - a

T_n - Nth Term of Progression?S_n - Sum of First N Terms of Progression?n - Index N of Progression?a - First Term of Progression?

Nth Term of Arithmetic Progression given Sum of First N Terms Example

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Here is how the Nth Term of Arithmetic Progression given Sum of First N Terms equation looks like with Units.

Here is how the Nth Term of Arithmetic Progression given Sum of First N Terms equation looks like.

163.6667 = (\frac{2 \cdot 500}{6}) - 3

163.6667 = (\frac{2 \cdot 500}{6}) - 3

163.6667 = (\frac{2 \cdot 500}{6}) - 3

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Nth Term of Arithmetic Progression given Sum of First N Terms Solution

Follow our step by step solution on how to calculate Nth Term of Arithmetic Progression given Sum of First N Terms?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

T n = (\frac{2 \cdot 500}{6}) - 3

Next Step Prepare to Evaluate

∴

T n = (\frac{2 \cdot 500}{6}) - 3

Next Step Evaluate

∴

T n = 163.666666666667

LAST Step Rounding Answer

∴

T n = 163.6667

Nth Term of Arithmetic Progression given Sum of First N 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

Sum of First N Terms of Progression

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

Symbol: S_n

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Sum of First N Terms 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

First Term of Progression

The First Term of Progression is the term at which the given Progression starts.

Symbol: a

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find First Term of Progression

Other Formulas to find Nth Term of Progression

Go Nth Term of Arithmetic Progression

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

Go Nth Term of Arithmetic Progression given Pth and Qth Terms

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})

Go Nth Term of Arithmetic Progression given Last Term

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

Other formulas in Nth Term of Arithmetic Progression category

Go Nth Term from End of Arithmetic Progression

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

Go Nth Term from End of Arithmetic Progression given Last Term

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

How to Evaluate Nth Term of Arithmetic Progression given Sum of First N Terms?

Nth Term of Arithmetic Progression given Sum of First N Terms evaluator uses Nth Term of Progression = ((2*Sum of First N Terms of Progression)/Index N of Progression)-First Term of Progression to evaluate the Nth Term of Progression, 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. Nth Term of Progression is denoted by T_n symbol.

How to evaluate Nth Term of Arithmetic Progression given Sum of First N Terms using this online evaluator? To use this online evaluator for Nth Term of Arithmetic Progression given Sum of First N Terms, enter Sum of First N Terms of Progression (S_n), Index N of Progression (n) & First Term of Progression (a) and hit the calculate button.

FAQs on Nth Term of Arithmetic Progression given Sum of First N Terms

What is the formula to find Nth Term of Arithmetic Progression given Sum of First N Terms?

The formula of Nth Term of Arithmetic Progression given Sum of First N Terms is expressed as Nth Term of Progression = ((2*Sum of First N Terms of Progression)/Index N of Progression)-First Term of Progression. Here is an example- 530.3333 = ((2*500)/6)-3.

How to calculate Nth Term of Arithmetic Progression given Sum of First N Terms?

With Sum of First N Terms of Progression (S_n), Index N of Progression (n) & First Term of Progression (a) we can find Nth Term of Arithmetic Progression given Sum of First N Terms using the formula - Nth Term of Progression = ((2*Sum of First N Terms of Progression)/Index N of Progression)-First Term 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
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))
Nth Term of Progression=First Term of Progression+(Index N of Progression-1)*((Last Term of Progression-First Term of Progression)/(Number of Total Terms of Progression-1))

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Nth Term of Arithmetic Progression given Sum of First N Terms Formula

​GoNth Term of Arithmetic Progression Formula

​GoNth Term of Arithmetic Progression given Pth and Qth Terms Formula

Nth Term of Arithmetic Progression given Sum of First N Terms Example

Nth Term of Arithmetic Progression given Sum of First N Terms Solution

Nth Term of Arithmetic Progression given Sum of First N 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 Sum of First N Terms?

FAQs on Nth Term of Arithmetic Progression given Sum of First N Terms

Variable Name

GoNth Term of Arithmetic Progression Formula

GoNth Term of Arithmetic Progression given Pth and Qth Terms Formula