Number of terms in a Series (AP)

Arithmetic series is a collection of numbers in an order having certain characteristics lets say, common difference or common multiple factors.

Often we are given a series of numbers, and are asked how many terms are there is this series.
For example- : let’s say you are given a series of numbers of 25,30,35,40,…………………..120 and you are asked to find many terms are in the whole series.

There is a very simple and easy way to find that. You just have to follow certain steps.

Step 1 – Find the difference between the first and last terms of the series.
Step 2 – Divide the calculated difference with the common difference between the two successive terms.
Step 3 – Add 1 to the answer.
Step 4 – If the final answer is a whole number, then it is your answer
If not a whole number, then the nearest lowest whole number is your answer.

Number Of Terms In An Arithmetic Progression Series In Algebra

Consider an example.

Find how many terms are there in the series 28, 35, 42, 49, ………….., 135 ?

Let’s Solve this-

Step 1 – 135 – 28 = 107
Step 2 – 107 / 7 = 15.28
Step 3 – 15.28 + 1 = 16.28
Step 4 – Now since 16.28 is not a whole number, so the nearest lowest whole number to 16.28 is 16.

So the series contains 16 terms.

142 Number Of Terms In An Arithmetic Progression Series In Algebra

Practice for more-

Find the number of terms in the series.

1) 23,29,35,41,………….,162
2) 87,96,105,114,…………….293
3) 122, 135, 148………………..459.

In this way, we can calculate the number of terms in an arithmetic series. I hope this article helped in understanding the concept.

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