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  • The sum of four numbers of an AP is 20 and sum of their squares is 120. Find the numbers Option: 1 2,4,6,8

The sum of four numbers of an AP is 20 and sum of their squares is 120. Find the numbers 

Option: 1

2,4,6,8


Option: 2

1,3,5,7


Option: 3

2,5,8,11


Option: 4

3,4,5,6


Answers (1)

best_answer

Selection of terms

If we have to take 4 terms in an AP, whose sum is known, we take them as

a - 3d, a - d, a + d, a + 3d

 

In this Question,

Let the numbers be a - 3d, a - d, a + d, a + 3d

Sum = 4a = 20 \Rightarrow a = 5

Also sum of squares condition:

\Rightarrow \left (a - 3d \right )^{2}+\left (a - d \right )^{2}+ \left (a + d \right )^{2}+ \left (a + 3d \right )^{2}= 120

4a^{2}+20d^{2}=120\Rightarrow 20d^2=20\Rightarrow d=\pm 1

So AP will be 2,4,6,8 (when d=1), or 8,6,4,2 (when d=-1)

Posted by

Ritika Kankaria

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