Question

If the sum of three consecutive terms of an A.P. is 51 and the product of last and first term is 273, then the numbers are.

• A. 21, 17, 13
• B. 20, 16, 12
• C. 22, 18, 14
• D. 24, 20, 16

Answer 1

Answer: (A)

21, 17, 13

Answer 2

Let consecutive terms of an A.P. are $a - d , a , a + d$.

Under given condition, $( a - d ) + a + ( a + d ) = 51$

$\Rightarrow$ $a = 17$ and$( a - d ) ( a + d ) = 273$ $\Rightarrow$ $a ^ { 2 } - d ^ { 2 } = 273$

$\Rightarrow$ $- d ^ { 2 } = 273 - 289$ $\Rightarrow$ $d = 4$

Hence consecutive terms are 13, 17, 21.

Trick : Both conditions are satisfied by (1) 21, 17, 13.