Question

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Find 4 numbers in AP whose sum is 20 and the sum of whose squares is 120.

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Answer 1

Answer:

Let the numbers be (a−3d),(a−d),(a+d),(a+3d).

 Then, Sum of numbers =20

⟹(a−3d)+(a−d)+(a+d)+(a+3d)=20⟹4a=20⟹a=5

It is given that, sum of the squares =120

⟹(a−3d)2+(a−d)2+(a+d)2+(a+3d)2=120

⟹4a2+20d2=120

⟹a2+5d2=30

⟹25+5d2=30

⟹5d2=5⟹d=±1

If d=1, the, the numbers are 2,4,6,8.

If d=−1, then the numbers are 8,6,4,2.

Thus, the numbers are 2,4,6,8 or 8,6,4,2.

Step-by-step explanation:

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Answer 2

Answer:

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