Question

Find four numbers in AP whose sum is 20 and the sum of whose square is 120

Answer 1

Heya !!!

Let the required numbers be (A - 3D ) , ( A - D ) , ( A + D ) and ( A + 3D )

According to question,

( A - 3D ) + ( A - D ) + ( A + D ) + ( A + 3D ) = 20

4A = 20

A = 20/4

A = 5

And,

(A - 3D)² + ( A - D)² + (A + D)² + (A + 3D )² = 120

=> 4 ( A² + 5D² ) = 120

=> (A² + 5D² ) = 30

=> (5)² + 5D² = 30

=> 25 + 5D² = 30

=> 5D² = 30-25

=> 5D² = 5

=> D² = 1

=> D = ✓1

=> D = + 1 or -1

Thus,

A = 5 and D = ‡1

Hence,

Required numbers are ( 2,4,6,8).

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