Question

Find three consecutive terms in an A.P. whose sum is 27 and their product is 504.​

Answer 1

Answer:

Let's assume that three consecutive terms are a-d, a, a+ d.

Given,

Sum of three consecutive terms = 27

Product of three consecutive terms = 504

( a - d) + a + (a + d) = 27

=> 3a = 27

=> a = 9

( a - d) × a × ( a + d) = 504

=> ( 9 - d) × 9 × ( 9 + d) = 504

$= > 81 - d {}^{2} = 56$

$= > d { }^{2} = 81 - 56$

$d {}^{2} = 25$

=> d = +, - 5

When d = 5

The terms are 9,14,19

When d = -5

The terms are 9,4,-1