Question

The sum of three numbers ii an ap is 24 and product is440.its middle term will be

Answer 1

Hi Mate !!


Let ap be

( a - d ) , a ( a + d )
Where a is the first term and d is the common difference.


• Sum is 24

a - b + a + a + b = 24

3a = 24

a = 8

• Their product is 440

( a - d ) × a × ( a + d ) = 440

( a² - d² ) a = 440

( 8² - d² )8 = 440

8³ - 8d² = 440

512 - 8d² = 440

- 8d² = 440 - 512

- 8d² = - 72

d² = 9

d = √9

d = ±3

_________________

Then AP's are :-

If a = 8 and d = 3

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

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

5 , 8 , 11

___________

If a = 8 and d = - 3

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

11 , 8 , 5