Last Term of Arithmetic Progression given Nth Term Calculator

✖The First Term of Progression is the term at which the given Progression starts.ⓘ First Term of Progression [a]			+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 Progression [T_n]			+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 Arithmetic Progression given Nth Term [l]

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Formula

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Last Term of Arithmetic Progression given Nth Term

Formula

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

Example

`"105.6"="3"+("10"-1)*(("60"-"3")/("6"-1))`

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Last Term of Arithmetic Progression given Nth Term Solution

STEP 0: Pre-Calculation Summary

Formula Used

Last Term of Progression = First Term of Progression+(Number of Total Terms of Progression-1)*((Nth Term of Progression-First Term of Progression)/(Index N of Progression-1))
l = a+(n_Total-1)*((T_n-a)/(n-1))
This formula uses 5 Variables

Variables Used

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

STEP 1: Convert Input(s) to Base Unit

First Term of Progression: 3 --> No Conversion Required
Number of Total Terms of Progression: 10 --> No Conversion Required
Nth Term of Progression: 60 --> No Conversion Required
Index N of Progression: 6 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

l = a+(n_Total-1)*((T_n-a)/(n-1)) --> 3+(10-1)*((60-3)/(6-1))

Evaluating ... ...

l = 105.6

STEP 3: Convert Result to Output's Unit

105.6 --> No Conversion Required

FINAL ANSWER

105.6 <-- Last Term of Progression

(Calculation completed in 00.004 seconds)

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< 5 Last Term of Arithmetic Progression Calculators

Last Term of Arithmetic Progression given Pth and Qth Terms

Go Last 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))+(Number of Total Terms of Progression-1)*((Qth Term of Progression-Pth Term of Progression)/(Index Q of Progression-Index P of Progression))

Last Term of Arithmetic Progression given Nth Term

Go Last Term of Progression = First Term of Progression+(Number of Total Terms of Progression-1)*((Nth Term of Progression-First Term of Progression)/(Index N of Progression-1))

Last Term of Arithmetic Progression given Sum of Last N Terms

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

Last Term of Arithmetic Progression given Sum of Total Terms

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

Last Term of Arithmetic Progression

Go Last Term of Progression = First Term of Progression+((Number of Total Terms of Progression-1)*Common Difference of Progression)

Last Term of Arithmetic Progression given Nth 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 Last Term of Arithmetic Progression given Nth Term?

Last Term of Arithmetic Progression given Nth Term calculator uses Last Term of Progression = First Term of Progression+(Number of Total Terms of Progression-1)*((Nth Term of Progression-First Term of Progression)/(Index N of Progression-1)) to calculate the Last Term of Progression, 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. Last Term of Progression is denoted by l symbol.

How to calculate Last Term of Arithmetic Progression given Nth Term using this online calculator? To use this online calculator for Last Term of Arithmetic Progression given Nth Term, enter First Term of Progression (a), Number of Total Terms of Progression (n_Total), Nth Term of Progression (T_n) & Index N of Progression (n) and hit the calculate button. Here is how the Last Term of Arithmetic Progression given Nth Term calculation can be explained with given input values -> 82.8 = 3+(10-1)*((60-3)/(6-1)).

FAQ

What is 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 and is represented as l = a+(n_Total-1)*((T_n-a)/(n-1)) or Last Term of Progression = First Term of Progression+(Number of Total Terms of Progression-1)*((Nth Term of Progression-First Term of Progression)/(Index N of Progression-1)). The First Term of Progression is the term at which the given Progression starts, The Number of Total Terms of Progression is the total number of terms present in the given sequence of Progression, The Nth Term of Progression is the term corresponding to the index or position n from the beginning in the given 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.

How to calculate 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 is calculated using Last Term of Progression = First Term of Progression+(Number of Total Terms of Progression-1)*((Nth Term of Progression-First Term of Progression)/(Index N of Progression-1)). To calculate Last Term of Arithmetic Progression given Nth Term, you need First Term of Progression (a), Number of Total Terms of Progression (n_Total), Nth Term of Progression (T_n) & Index N of Progression (n). With our tool, you need to enter the respective value for First Term of Progression, Number of Total Terms of Progression, Nth Term of Progression & Index N 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 Last Term of Progression?

In this formula, Last Term of Progression uses First Term of Progression, Number of Total Terms of Progression, Nth Term of Progression & Index N of Progression. We can use 4 other way(s) to calculate the same, which is/are as follows -

Last Term of Progression = First Term of Progression+((Number of Total Terms of Progression-1)*Common Difference of Progression)
Last Term of Progression = (Sum of Last N Terms of Progression/Index N of Progression-(Common Difference of Progression*(1-Index N of Progression))/2)
Last 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))+(Number of Total Terms of Progression-1)*((Qth Term of Progression-Pth Term of Progression)/(Index Q of Progression-Index P of Progression))
Last Term of Progression = ((2*Sum of Total Terms of Progression)/Number of Total Terms of Progression)-First Term of Progression

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