Question

Find whether 55 is a term of the A.P. 7, 10, 13,... or not. If yes, find which term is it.

Answer 1

Yes.

Let the first term, common difference and the number of terms of an AP are a, d and n respectively.

Let the n^th term of an AP be 55

i.e., T_n = 55

We know that,

The n^th term of an AP,

T_n = a + (n – 1)d   ...(i)

Given that,

First term (a) = 7

and common difference (d) = 10 – 7 = 3

From equation (i),

55 = 7 + (n – 1) × 3

⇒ 55 = 7 + 3n – 3

⇒ 55 = 4 + 3n

⇒ 3n = 51

∴ n = 17

Since, n is a positive integer.

So, 55 is a term of the AP.

Since, n = 17

Therefore, 17^th term of an AP is 55.