Question

There are five terms in AP. Sum of the squares of extremes is 104 and sum of terms is 30 then find common difference (d)?

Answer 1

HELLO DEAR,

let common difference be ( d ),

and first term is ( a ).

let the five terms be (a + 2d) , (a + b) , a , (a - d) , (a - 2d)

GIVEN:- Sum of the squares of extremes is 104 .

so,

(a + 2d)² + (a - 2d)² = 104

=> a² + 4d² + 4ad + a² + 4d² - 4ad = 104

=> 2a² + 8d² = 104--------------( 1 )

also,

sum of terms is 30

so, a + 2d + a + d + a + a - d + a - 2d = 30

=> 5a = 30

=> a = 6 [ put in ------ ( 1 ) ]

we get,

2a² + 8d² = 104

=> a² + 4d² = 52

=> 6² + 4d² = 52

=> 4d² = 52 - 36

=> 4d² = 16

=> d² = 4

=> d = ±2

I HOPE IT'S HELP YOU DEAR,

THANKS

Answer 2

Answer:

PLEASE CHECK YOUR ANSWER CAREFULLY

HOPE IT HELPS TO U

PLEASE MARK ME AS BRAINLIST