Question

If the sum of three consecutive terms of an increasing A.P. is 51 and the product of the first and third of these terms is 273, then the third term is 

A. 13 

B. 9 

C. 21 

D. 17

Answer 1

Correct answer is C. 21.

Let 3 consecutive terms A.P is a –d, a, a + d. and the sum is 51 

So, (a –d) + a + (a + d) = 51 

3a –d + d = 51 

3a = 51 

a = 17 

The product of first and third terms = 273 

So, (a –d) (a + d) = 273

 a² –d² = 273 

17² –d² = 273 

289 –d² = 273 

d² = 289 –273 

d² = 16 

d = 4 

Third term = a + d = 17 + 4 = 21