Question

HELLO GUYS................................

CLASS 10
chapter ARITHMETIC PROGRESSIONS

QUESTION DIFFICULTLY:HARD

Q)FIND FOUR NUMBERS IN AP WHOSE SUM IS 28 AND THE SUM OF WHOSE SQUARES IS 216.

EXPLAIN IN DETAIL​

Answer 1

As we need four number let the numbers be

a-3d , a-d , a+d , a+3d [the difference is 2d]

their sum is 28

I.e. 4a = 28

a = 7

a² + 9d² + a² + d² + a² + d² + a² + 9d² = 216

[ other terms get cancelled while adding after expansion]

196 + 20d² = 216

d = +1 or -1

so the numbers are

4, 6 , 8 ,10 [ any order according to the d you take]