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.

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.

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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