Question

find four consecutive terms in A.P such that the sum of middle two terms is 18 and the product of the two end terms is 45​

Answer 1

a-3d, a+d , a-d , a+3d.

given the sum of the middle terms is 18.

2a = 18

a = 9

(a-3d)2 = 45

a² - 9d² = 45

9² - 9d² = 45

81 - 9d² = 45

9d² = 81 - 45

9d² = 36

d = 2 or -2

Putting a = 9 and d = -2 or 2 we get four terms  

3, 7, 11 and 15

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