Find the number of terms in the following AP:
7, 13, 19, ..., 205

Given: AP series 7, 13, 19, ..., 205.

To find: Here we have to find the number of terms in the given AP.

Solution:

First term (a) = 7

Common difference (d) = 13 $−$ 7 = 6

Last term (a_n) = 205

Let the last term be the n^th term

We know that the n^th term of the arithmetic progression is given by (a $+$ (n $−$ 1)d).

Therefore,

a $+$ (n $−$ 1)d = 205

7 $+$ (n $−$ 1)6 = 205

7 $−$ 6 $+$ 6n = 205

1 $+$ 6n = 205

6n = 205 $−$ 1

n = $\frac{204}{6}$

​

n = 34

So, number of terms in the given sequence is 34.

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Updated on: 10-Oct-2022

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