First Term of Arithmetic Progression Calculator

✖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 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 [a]

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Formula

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First Term of Arithmetic Progression

Formula

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

Example

`"40"="60"-(("6"-1)*"4")`

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First Term of Arithmetic Progression Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

Nth Term of Progression: 60 --> 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

a = T_n-((n-1)*d) --> 60-((6-1)*4)

Evaluating ... ...

a = 40

STEP 3: Convert Result to Output's Unit

40 --> No Conversion Required

FINAL ANSWER

40 <-- First Term of Progression

(Calculation completed in 00.004 seconds)

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Created by Shivam Dixit

BSS Education Centre Kanpur (BSS College), Kanpur

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Indian Institute of technology (IIT-BHU), Varanasi

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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)

< 11 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))

Sum of Terms from Pth to Qth Terms of Arithmetic Progression

Go Sum of Terms from Pth to Qth Terms of Progression = ((Index Q of Progression-Index P of Progression+1)/2)*((2*First Term of Progression)+((Index P of Progression+Index Q of Progression-2)*Common Difference of Progression))

Sum of Last N Terms of Arithmetic Progression

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

Sum of First N Terms of Arithmetic Progression

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))

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

Common Difference of Arithmetic Progression given Last Term

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

Sum of Total Terms of Arithmetic Progression given Last Term

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

Number of Terms of Arithmetic Progression

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

First Term of Arithmetic Progression

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

Common Difference of Arithmetic Progression

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

First Term of Arithmetic Progression Formula

First Term of Progression = Nth Term of Progression-((Index N of Progression-1)*Common Difference of Progression)
a = T_n-((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 First Term of Arithmetic Progression?

First Term of Arithmetic Progression calculator uses First Term of Progression = Nth Term of Progression-((Index N of Progression-1)*Common Difference of Progression) to calculate the First Term of Progression, The First Term of Arithmetic Progression formula is defined as the term at which the given Arithmetic Progression starts. First Term of Progression is denoted by a symbol.

How to calculate First Term of Arithmetic Progression using this online calculator? To use this online calculator for First Term of Arithmetic Progression, enter Nth Term of Progression (T_n), Index N of Progression (n) & Common Difference of Progression (d) and hit the calculate button. Here is how the First Term of Arithmetic Progression calculation can be explained with given input values -> 1355 = 60-((6-1)*4).

FAQ

What is First Term of Arithmetic Progression?

The First Term of Arithmetic Progression formula is defined as the term at which the given Arithmetic Progression starts and is represented as a = T_n-((n-1)*d) or First Term of Progression = Nth Term of Progression-((Index N of Progression-1)*Common Difference 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 & 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?

The First Term of Arithmetic Progression formula is defined as the term at which the given Arithmetic Progression starts is calculated using First Term of Progression = Nth Term of Progression-((Index N of Progression-1)*Common Difference of Progression). To calculate First Term of Arithmetic Progression, you need Nth Term of Progression (T_n), Index N of Progression (n) & Common Difference of Progression (d). With our tool, you need to enter the respective value for Nth 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 First Term of Progression?

In this formula, First Term of Progression uses Nth Term of Progression, Index N 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 = Last Term of Progression-((Number of Total Terms 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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