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Four numbers are in A.P. If their sum is...

Four numbers are in A.P. If their sum is 20 and the sum of their squares is 120, then the middle terms are

A

2, 4

B

4, 6

C

6, 8

D

8, 10

Text Solution

Verified by Experts

The correct Answer is:
B
Let the number are `a - 3d, a - d, a + d, a + 3d`
given, `a - 3d + a - d + a + d + a + 3d = 20 " " rArr 4a = 20 rArr a = 5`
and `(a - 3d)^(2) + (a - d)^(2) + (a + d)^(2) + (a + 3d)^(2) = 120 rArr 4a^(2) + 20d^(2) = 120`
`rArr 4 xx 5^(2) + 20 d^(2) = 120 " " rArr d^(2) = 1 rArr d = +- 1`
Hence number 2,4,6,8 or 8,6,4,2
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