Question

7.In an A.P. sum of three consecutive terms is 27 and their products is 504, find the terms

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Answer 1

Answer:

Let the 3 terms in AP be

a-d, a, a+d

So, Sum of these 3 terms is=

a - d + a + a + d = 3a

So, 3a = 27

a = 9

Also, we are given product of numbers i.e

(a - d) x a x (a + d) = 504

(a² - d²) x a = 504

Putting a = 9, we have

(9² - d²) x 9 = 504

81 - d² = 504/9 = 56

d² = 81 - 56 = 25

so, d = 5 or -5

So, our terms are

9-5, 9, 9+5

or

9+5, 9, 9-5

So, our terms are 4, 9, 14 or 14, 9, 4 with d = 5 or -5