Question

The 59th term of an A.P. is 449 and the 449th term is 59. Which term is equal to 0?

(a) 501st term 

(b) 502nd term 

(c) 508th term 

(d) 509th term

Answer 1

Answer : (c) 508th term

Let a and d be the first term and common difference of the given A.P. 

Then, 

a + 58 d = 449 ...(i) 

a + 448 d = 59 ...(ii)

Solving eqns (i) and (ii) simultaneously, we get 

a = 507, d = – 1 

Now assume that the nth term is zero.

∴ 0 = a + (n – 1)d 

⇒ 0 = 507 + (n – 1) (– 1) 

⇒ 507 = n – 1 

⇒ n = 508. 

Thus 508th term will be zero.