Nth Term of Arithmetic Progression given Last Term 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 Last Term of Progression is the term at which the given Progression terminates.ⓘ Last Term of Progression [l]			+10% -10%
✖The Number of Total Terms of Progression is the total number of terms present in the given sequence of Progression.ⓘ Number of Total Terms of Progression [n_Total]			+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 given Last Term [T_n]

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Formula

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Nth Term of Arithmetic Progression given Last Term

Formula

`"T"_{"n"} = "a"+("n"-1)*(("l"-"a")/("n"_{"Total"}-1))`

Example

`"56.88889"="3"+("6"-1)*(("100"-"3")/("10"-1))`

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Nth Term of Arithmetic Progression given Last Term Solution

STEP 0: Pre-Calculation Summary

Formula Used

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))
T_n = a+(n-1)*((l-a)/(n_Total-1))
This formula uses 5 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.
Last Term of Progression - The Last Term of Progression is the term at which the given Progression terminates.
Number of Total Terms of Progression - The Number of Total Terms of Progression is the total number of terms present in the given sequence of Progression.

STEP 1: Convert Input(s) to Base Unit

First Term of Progression: 3 --> No Conversion Required
Index N of Progression: 6 --> No Conversion Required
Last Term of Progression: 100 --> No Conversion Required
Number of Total Terms of Progression: 10 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

T_n = a+(n-1)*((l-a)/(n_Total-1)) --> 3+(6-1)*((100-3)/(10-1))

Evaluating ... ...

T_n = 56.8888888888889

STEP 3: Convert Result to Output's Unit

56.8888888888889 --> No Conversion Required

FINAL ANSWER

56.8888888888889 ≈ 56.88889 <-- Nth Term of Progression

(Calculation completed in 00.004 seconds)

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< 6 Nth Term of Arithmetic Progression Calculators

Nth Term of Arithmetic Progression given Pth and Qth Terms

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 of Arithmetic Progression given Last Term

Go 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))

Nth Term from End of Arithmetic Progression

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 from End of Arithmetic Progression given Last Term

Go Nth Term from End of Progression = Last Term of Progression-(Index N of Progression-1)*Common Difference of Progression

Nth Term of Arithmetic Progression given Sum of First N Terms

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

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

Nth Term of Arithmetic Progression given Last Term Formula

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 given Last Term?

Nth Term of Arithmetic Progression given Last Term calculator uses 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)) to calculate the Nth Term of Progression, 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. Nth Term of Progression is denoted by T_n symbol.

How to calculate Nth Term of Arithmetic Progression given Last Term using this online calculator? To use this online calculator for Nth Term of Arithmetic Progression given Last Term, enter First Term of Progression (a), Index N of Progression (n), Last Term of Progression (l) & Number of Total Terms of Progression (n_Total) and hit the calculate button. Here is how the Nth Term of Arithmetic Progression given Last Term calculation can be explained with given input values -> 72.28571 = 3+(6-1)*((100-3)/(10-1)).

FAQ

What is 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 and is represented as T_n = a+(n-1)*((l-a)/(n_Total-1)) or 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)). 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 Last Term of Progression is the term at which the given Progression terminates & The Number of Total Terms of Progression is the total number of terms present in the given sequence of Progression.

How to calculate 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 is calculated using 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)). To calculate Nth Term of Arithmetic Progression given Last Term, you need First Term of Progression (a), Index N of Progression (n), Last Term of Progression (l) & Number of Total Terms of Progression (n_Total). With our tool, you need to enter the respective value for First Term of Progression, Index N of Progression, Last Term of Progression & Number of Total Terms 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, Last Term of Progression & Number of Total Terms of Progression. We can use 3 other way(s) to calculate the same, which is/are as follows -

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

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