Question

Find three numbers in AP whose sum is 15 and product is 80.

Answer 1

let a - d , a , a + d are three terms of an AP

according to the problem given;

sum of the terms = 15

a - d + a + a + d = 15

3a = 15

a = 15 / 3

a = 5

product = 80

( a - d ) a ( a + d ) = 80

( a² - d² ) a = 80

( 5² - d² ) 5 = 80

25 - d² = 80 /5

25 - d² = 16

- d² = - 9

d² = 3²

d = ± 3

Therefore,

a = 5 , d = ±3

required 3 terms are

a - d = 5 - 3 = 2

a = 5

a+ d = 5 + 3 = 8

( 2 , 5 , 8 ) or ( 8 , 5 , 2 )