First Term of Arithmetic Progression given Last Term Calculator

✖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 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 First Term of Progression is the term at which the given Progression starts.ⓘ First Term of Arithmetic Progression given Last Term [a]

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Formula

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First Term of Arithmetic Progression given Last Term

Formula

`"a" = "l"-(("n"_{"Total"}-1)*"d")`

Example

`"64"="100"-(("10"-1)*"4")`

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First Term of Arithmetic Progression given Last Term Solution

STEP 0: Pre-Calculation Summary

Formula Used

First Term of Progression = Last Term of Progression-((Number of Total Terms of Progression-1)*Common Difference of Progression)
a = l-((n_Total-1)*d)
This formula uses 4 Variables

Variables Used

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

Last Term of Progression: 100 --> No Conversion Required
Number of Total Terms of Progression: 10 --> No Conversion Required
Common Difference of Progression: 4 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

a = l-((n_Total-1)*d) --> 100-((10-1)*4)

Evaluating ... ...

a = 64

STEP 3: Convert Result to Output's Unit

64 --> No Conversion Required

FINAL ANSWER

64 <-- First Term of Progression

(Calculation completed in 00.004 seconds)

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< 3 First Term of Arithmetic Progression Calculators

First Term of Arithmetic Progression given Pth and Qth Terms

Go First 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)

First Term of Arithmetic Progression given Last Term

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

First Term of Arithmetic Progression

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

First Term of Arithmetic Progression given Last Term Formula

First Term of Progression = Last Term of Progression-((Number of Total Terms of Progression-1)*Common Difference of Progression)
a = l-((n_Total-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 First Term of Arithmetic Progression given Last Term?

First Term of Arithmetic Progression given Last Term calculator uses First Term of Progression = Last Term of Progression-((Number of Total Terms of Progression-1)*Common Difference of Progression) to calculate the First Term of Progression, The First Term of Arithmetic Progression given Last Term formula is defined as the term at which the given Arithmetic Progression starts, calculated using the last term of the Arithmetic Progression. First Term of Progression is denoted by a symbol.

How to calculate First Term of Arithmetic Progression given Last Term using this online calculator? To use this online calculator for First Term of Arithmetic Progression given Last Term, enter Last Term of Progression (l), Number of Total Terms of Progression (n_Total) & Common Difference of Progression (d) and hit the calculate button. Here is how the First Term of Arithmetic Progression given Last Term calculation can be explained with given input values -> 72 = 100-((10-1)*4).

FAQ

What is First Term of Arithmetic Progression given Last Term?

The First Term of Arithmetic Progression given Last Term formula is defined as the term at which the given Arithmetic Progression starts, calculated using the last term of the Arithmetic Progression and is represented as a = l-((n_Total-1)*d) or First Term of Progression = Last Term of Progression-((Number of Total Terms of Progression-1)*Common Difference of 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 & The Common Difference of Progression is the difference between two consecutive terms of a Progression, which is always a constant.

How to calculate First Term of Arithmetic Progression given Last Term?

The First Term of Arithmetic Progression given Last Term formula is defined as the term at which the given Arithmetic Progression starts, calculated using the last term of the Arithmetic Progression is calculated using First Term of Progression = Last Term of Progression-((Number of Total Terms of Progression-1)*Common Difference of Progression). To calculate First Term of Arithmetic Progression given Last Term, you need Last Term of Progression (l), Number of Total Terms of Progression (n_Total) & Common Difference of Progression (d). With our tool, you need to enter the respective value for Last Term of Progression, Number of Total Terms 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 First Term of Progression?

In this formula, First Term of Progression uses Last Term of Progression, Number of Total Terms of Progression & Common Difference of Progression. We can use 2 other way(s) to calculate the same, which is/are as follows -

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

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