Question

Find three numbers in an AP whose sum is 9 and the product is -165

Answer 1

Hi Mate !!


Let the three No. of AP be

( a - d ) , a , ( a + d )

Where , a is first term
and d is common difference.


• Sum of the no. is 9

a - d + a + a + d = 9

3a = 9

a = 9/3

a = 3


• Product of the no. is ( - 165 )

( a - d ) × a × ( a + d ) = ( - 165 )

[ Using identity ( x - y ) ( x + y ) = x² - y² ]

( a² - d² ) × a = ( - 165 )

( 3 )² - d² = -165/3

9 - d² = ( - 55 )

- d² = ( - 55 - 9 )

d² = 64

d = √64

d = ± 8

♯ The terms of the AP are :-

• If a = 3 and d = 8

( a - d ) , a , ( a + d )

( 3 - 8 ) , 3 , ( 3 + 8 )

- 5 , 3 , 11

• If a = 3 and d = ( - 8 )

( a - d ) , a , ( a + d )

( 3 + 8 ) , 3 , ( 3 - 8 )

11 , 3 , - 5