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

How many terms are there in the A.P.?

7, 13, 19, ..., 205.

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#### Solution

7, 13, 19, …, 205

For this A.P.,

a = 7

d = a_{2} − a_{1} = 13 − 7 = 6

Let there are n terms in this A.P.

a_{n} = 205

We know that

a_{n} = a + (n − 1) d

Therefore, 205 = 7 + (n − 1) 6

198 = (n − 1) 6

33 = (n − 1)

n = 34

Therefore, this given series has 34 terms in it.

Concept: nth Term of an AP

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