Question

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

I. 7, 13, 19, …, 205

II.

Answer 1

I. 7, 13, 19, …, 205

For this A.P.,

a = 7

d = a₂ − a₁ = 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.

II.

For this A.P.,

Let there are n terms in this A.P.

Therefore, a_n = −47 and we know that,

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