Question

The sum of 3 numbers of an ap is 27 their product is 405 find ap

Answer 1

Let the three terms of AP be

a,a+d and a-d

So sum of the terms is...

a + d + a + a-d = 27

3a = 27

a = 9

And also according to question....

a×a+d×a-d = 405

Putting value of a in this we get..

(9)× (9-d)×(9+d) = 405

(9-d)(9+d) = 45

9^2 - d^2 = 45

81+d^2 = 45

d^2 = 36

d= ±6

So a= 9 and d = ±6

HOPE THIS HELP YOU ☺☺

Answer 2

Let the first term of ap series is a and common difference is d

let the three terms are a-d , a , a+d

according to the question:

(a-d)+a+(a+d)=27........(1) and (a-d)*a*(a+d)=405..........................(2)

solving equation 1 we get 3a=27 or a=9

put the value of a in eqn. 2 we get

(9-d)*9*(9+d)=405

9*(81-d^2)=405        apply (a-b)*(a+b)= a^2-b^2

on solving this we get d=+6 or -6

if we take d=6 then three terms are 3,9,12

if we take d=-6 then three terms are 15, 9,3