If the sum of three consecutive terms of an increasing A.P. is 51 and

1.	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» 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

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»

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