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 = ((Tn-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 = ((Tn-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 00.004 seconds)

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Created by Mayank Tayal
National Institute of Technology (NIT), Durgapur
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4 Number of Terms in Arithmetic Progression Calculators

Number of Total Terms of Arithmetic Progression given Sum of Total Terms
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
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
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
Go Index N of Progression = ((Nth Term of Progression-First Term of Progression)/Common Difference of Progression)+1

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

Number of Terms of Arithmetic Progression Formula

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