Four numbers are in A.P. If their sum is 20 and the sum of their squares is 120, then the middle terms are
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
4 views
1 Answers
Correct Answer - 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
4 views
Answered