Question

find four numbers in AP whose sum is 8 and the square of sum is 196 and explain​

Answer 1

Solution

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Let the numbers be, a−3d,a−d,a+d,a+3d

Given,

a−3d+a−d+a+3d+a+d=28

⇒4a=28,

∴a=7

(a−3d)

2

+(a−d)

2

+(a+3d)

2

+(a+d)

2

=216

2(a

2

+9d

2

)+2(a

2

+d

2

)=216

4a

2

+20d

2

=216

4(7

2

)+20d

2

=216

⇒d=±1

for d=−1

the series is 7−3(−1),7−(−1),7−1,7−3⇒10,8,6,4

For d=1

the series is 7−3,7−1,7+1,7+3⇒4,6,8,10

Therefore the numbers are, 4,6,8,10

Hope it helps you Army!!!!

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