Number of Terms 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 First Term of Progression is the term at which the given Progression starts.ⓘ First Term of Progression [a]			+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 Index N of Progression is the value of n for the nth term or the position of the nth term in a Progression.ⓘ Number of Terms of Arithmetic Progression [n]

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Number of Terms of Arithmetic Progression Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

Variables Used

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.
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.
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
First Term of Progression: 3 --> No Conversion Required
Common Difference of Progression: 4 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

n = ((T_n-a)/d)+1 --> ((60-3)/4)+1

Evaluating ... ...

n = 15.25

STEP 3: Convert Result to Output's Unit

15.25 --> No Conversion Required

FINAL ANSWER

15.25 <-- Index N of Progression

(Calculation completed in 00.020 seconds)

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Created by Mayank Tayal

National Institute of Technology (NIT), Durgapur

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Birla Institute of Technology & Science (BITS), Hyderabad

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< Number of Terms in Arithmetic Progression Calculators

Number of Total Terms of Arithmetic Progression given Sum of Total Terms

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

Number of Total Terms of Arithmetic Progression

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

Number of Terms of Arithmetic Progression given Sum of First N Terms

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

Number of Terms of Arithmetic Progression

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

< 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

Number of Terms of Arithmetic Progression Formula

LaTeX Go

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

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 Number of Terms of Arithmetic Progression?

Number of Terms of Arithmetic Progression calculator uses Index N of Progression = ((Nth Term of Progression-First Term of Progression)/Common Difference of Progression)+1 to calculate the Index N of Progression, The Number of Terms of Arithmetic Progression formula is defined as the value of n for the nth term or the position of the nth term in an Arithmetic Progression. Index N of Progression is denoted by n symbol.

How to calculate Number of Terms of Arithmetic Progression using this online calculator? To use this online calculator for Number of Terms of Arithmetic Progression, enter Nth Term of Progression (T_n), First Term of Progression (a) & Common Difference of Progression (d) and hit the calculate button. Here is how the Number of Terms of Arithmetic Progression calculation can be explained with given input values -> 344 = ((60-3)/4)+1.

FAQ

What is Number of Terms of Arithmetic Progression?

The Number of Terms of Arithmetic Progression formula is defined as the value of n for the nth term or the position of the nth term in an Arithmetic Progression and is represented as n = ((T_n-a)/d)+1 or Index N of Progression = ((Nth Term of Progression-First Term of Progression)/Common Difference of Progression)+1. The Nth Term of Progression is the term corresponding to the index or position n from the beginning in the given Progression, The First Term of Progression is the term at which the given Progression starts & The Common Difference of Progression is the difference between two consecutive terms of a Progression, which is always a constant.

How to calculate Number of Terms of Arithmetic Progression?

The Number of Terms of Arithmetic Progression formula is defined as the value of n for the nth term or the position of the nth term in an Arithmetic Progression is calculated using Index N of Progression = ((Nth Term of Progression-First Term of Progression)/Common Difference of Progression)+1. To calculate Number of Terms of Arithmetic Progression, you need Nth Term of Progression (T_n), First Term of Progression (a) & Common Difference of Progression (d). With our tool, you need to enter the respective value for Nth Term of Progression, First Term 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 Index N of Progression?

In this formula, Index N of Progression uses Nth Term of Progression, First Term of Progression & Common Difference of Progression. We can use 1 other way(s) to calculate the same, which is/are as follows -

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

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