Question

in an AP sum of three consective term is 27 and their product is 504 find the terms ( three consecutive term in AP are a-d,a,a+d)

Answer 1

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

Answer 2

Hers is your solution

Given :-

sum of three consective term of ap is 27.

their product is 504

Let
The three numbers be a-d , a ,a+d.

a-d+a+a+d=27
3a=27
a=27/3
a=9

(a-d)×a×(a+d)=504

(a^2-d^2)a=504

(9^2-d^2)9=504

81-d^2 = 504/9

81-d^2= 56

d^2 = 81-56
d^2 = 25

d= + -5

If d=+5
Terms of A.p are 4,9,14

If d=-5
Terms of AP are 14,9,4

Thanks