Question

In an A.P. sum of three consecutive terms is 27 and their product is 504, find the terms. (Assume that three consecutive terms in A.P. are a - d , a, a + d.) Solve the word problem

Answer 1

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Answer 2

Let a - d , a , a + d are three

consecutive terms in A P

i ) Sum of three terms = 27

a-d+a+a+d = 27

=> 3a = 27

=> a = 27/3

=> a = 9

ii ) product of the terms = 504

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

=> (a² - d² ) a = 504

=> ( 9² - d² ) 9 = 504

=> 81 - d² = 504/9

=> 81 - d² = 56

=> -d² = 56 - 81

=>- d² = -25

=> d² = 25

d = ± 5 ,

Therefore ,

If a = 9 , d = 5,

Three terms are ,

a - d = 9 - 5 = 4,

a = 9 ,

a + d = 9 + 5 = 14

If a = 9 , d = -5

Three terms are ,

14 , 9 , 4

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