Math, asked by pawandeepkaur00, 10 months ago

The sum of four terms in AP is 32 and the sum of their squares is 336. Find the numbers​

Answers

Answered by syamsukesh
2

Answer:

a+a+d+a+2d+a+3d=32

4a+6d=32

2a+3d=16

squaring on both sides 4a^2+9d^2+12ad=256. 1st en

sum of their squares is 336

a^2+(a+d)^2+(a+2d)^2+(a+3d)^2=336

4a^2+14d^2+12ad=336 2nd eqn

solve 1 and 2

we will get d=4

a=2

the numbers are 2,6, 10,14

Answered by anitharathod27
2

Let the 4 terms be ,

( a - 3d ) , (a - d ) , ( a + d ) & ( a + 3d )

THEIR SUM IS 32 SO....

=>(a-d) + (a-3d) + (a+d) + (a+3d) = 32

=> 4a = 32

=> a = 8

SUM OF THEIR SQUARES IS 336 SO...

=> (a-d)² + (a-3d)² + (a+d)² + (a+3d)² = 336

=> 4a² + 20d² = 336

=> a² + 5d² = 84

=> 8² + 5d² = 84

=> 5d² = 84 - 64

=> 5d² = 20

=> d² = 20/5

=> d² = 4

=> d = 2

THUS,

a = 8

d = 2

AP = 8 , 10 , 12 , 14.....

HOPE IT HELPS !!

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