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Let a(1), a(2),....a(3) be an AP, S = su...

Let `a_(1), a_(2),....a_(3)` be an AP, `S = sum_(i = 1)^(30) a_(i) and T = sum_(i=1)^(15) a_((2i-1))`. If `a_(5) = 27 and S -2T = 75`, then `a_(10)` is equal to

A

42

B

57

C

52

D

47

Text Solution

Verified by Experts

The correct Answer is:
C
We have, `S = a_(1) + a_(2) + ...+ a_(30)`
`= 15 [2a_(1) + 29d]`...(i)
(where d is the common difference)
`[ :' S_(n) = (n)/(2) [2a + (n -1) d]]`
and `T = a_(1) + a_(3) + ...+ a_(29)`
`= (15)/(2) [2a_(1) + 14 xx 2d)]` ( `:'` common difference is 2d)
`rArr 2T = 15[2a_(1) + 28d]` ...(ii)
From Eqs. (i) and (iii), we get
`S - 2T = 15d = 75 " " [ :' S - 2T = 75]`
`rArr d = 5`
Now, `a_(10) = a_(5) + 5d`
`= 27 + 25 = 52`
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