Nth Term of Arithmetic Progression Calculator

✖The First Term of Progression is the term at which the given Progression starts.ⓘ First Term of Progression [a]			+10% -10%
✖The Index N of Progression is the value of n for the nth term or the position of the nth term in a Progression.ⓘ Index N of Progression [n]			+10% -10%
✖The Common Difference of Progression is the difference between two consecutive terms of a Progression, which is always a constant.ⓘ Common Difference of Progression [d]			+10% -10%

✖The Nth Term of Progression is the term corresponding to the index or position n from the beginning in the given Progression.ⓘ Nth Term of Arithmetic Progression [T_n]

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Nth Term of Arithmetic Progression Solution

STEP 0: Pre-Calculation Summary

Formula Used

Nth Term of Progression = First Term of Progression+(Index N of Progression-1)*Common Difference of Progression
T_n = a+(n-1)*d
This formula uses 4 Variables

Variables Used

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.
First Term of Progression - The First Term of Progression is the term at which the given Progression starts.
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.
Common Difference of Progression - The Common Difference of Progression is the difference between two consecutive terms of a Progression, which is always a constant.

STEP 1: Convert Input(s) to Base Unit

First Term of Progression: 3 --> No Conversion Required
Index N of Progression: 6 --> No Conversion Required
Common Difference of Progression: 4 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

T_n = a+(n-1)*d --> 3+(6-1)*4

Evaluating ... ...

T_n = 23

STEP 3: Convert Result to Output's Unit

23 --> No Conversion Required

FINAL ANSWER

23 <-- Nth Term of Progression

(Calculation completed in 00.020 seconds)

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Created by Mridul Sharma

Indian Institute of Information Technology (IIIT), Bhopal

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< Nth Term of Arithmetic Progression Calculators

Nth Term of Arithmetic Progression given Pth and Qth Terms

LaTeX Go 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 from End of Arithmetic Progression

LaTeX Go Nth Term from End of Progression = First Term of Progression+(Number of Total Terms of Progression-Index N of Progression)*Common Difference of Progression

Nth Term of Arithmetic Progression given Sum of First N Terms

LaTeX Go Nth Term of Progression = ((2*Sum of First N Terms of Progression)/Index N of Progression)-First Term of Progression

Nth Term of Arithmetic Progression

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

< Arithmetic Progression Calculators

Sum of First N Terms of Arithmetic Progression

LaTeX Go Sum of First N Terms of Progression = (Index N of Progression/2)*((2*First Term of Progression)+((Index N of Progression-1)*Common Difference of Progression))

Sum of Total Terms of Arithmetic Progression given Last Term

LaTeX Go Sum of Total Terms of Progression = (Number of Total Terms of Progression/2)*(First Term of Progression+Last Term of Progression)

Nth Term of Arithmetic Progression

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

Common Difference of Arithmetic Progression

LaTeX Go Common Difference of Progression = Nth Term of Progression-(N-1)th Term of Progression

Nth Term of Arithmetic Progression Formula

LaTeX Go

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

What is an Arithmetic Progression?

An Arithmetic Progression or simply AP is a sequence of numbers such that successive terms are obtained by adding a constant number to the first term. That fixed number is called the common difference of the Arithmetic Progression. For example, the sequence 2, 5, 8, 11, 14,... is an Arithmetic Progression with first term is 2 and common difference is 3. An AP is a convergent sequence if and only if the common difference is 0, otherwise an AP is always divergent.

How to Calculate Nth Term of Arithmetic Progression?

Nth Term of Arithmetic Progression calculator uses Nth Term of Progression = First Term of Progression+(Index N of Progression-1)*Common Difference of Progression to calculate the Nth Term of 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. Nth Term of Progression is denoted by T_n symbol.

How to calculate Nth Term of Arithmetic Progression using this online calculator? To use this online calculator for Nth Term of Arithmetic Progression, enter First Term of Progression (a), Index N of Progression (n) & Common Difference of Progression (d) and hit the calculate button. Here is how the Nth Term of Arithmetic Progression calculation can be explained with given input values -> 23 = 3+(6-1)*4.

FAQ

What is 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 and is represented as T_n = a+(n-1)*d or Nth Term of Progression = First Term of Progression+(Index N of Progression-1)*Common Difference of Progression. The First Term of Progression is the term at which the given Progression starts, The Index N of Progression is the value of n for the nth term or the position of the nth term in a Progression & The Common Difference of Progression is the difference between two consecutive terms of a Progression, which is always a constant.

How to calculate 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 is calculated using Nth Term of Progression = First Term of Progression+(Index N of Progression-1)*Common Difference of Progression. To calculate Nth Term of Arithmetic Progression, you need First Term of Progression (a), Index N of Progression (n) & Common Difference of Progression (d). With our tool, you need to enter the respective value for First Term of Progression, Index N of Progression & Common Difference of Progression and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Nth Term of Progression?

In this formula, Nth Term of Progression uses First Term of Progression, Index N of Progression & Common Difference of Progression. We can use 3 other way(s) to calculate the same, which is/are as follows -

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 = ((2*Sum of First N Terms of Progression)/Index N of Progression)-First Term 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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