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Question

Find the number of terms in each of the following A.P.

I. 7, 13, 19, …, 205

II.

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Solution

I. 7, 13, 19, …, 205

For this A.P.,

a = 7

d = a2a1 = 13 − 7 = 6

Let there are n terms in this A.P.

an = 205

We know that

an = 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.

II.

For this A.P.,

Let there are n terms in this A.P.

Therefore, an = −47 and we know that,

Therefore, this given A.P. has 27 terms in it.


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