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Let numbers a(1),a(2)…a(16) are in AP an...

Let numbers `a_(1),a_(2)…a_(16)` are in AP and `a_(1)+a_(4)+a_(7)+a_(10)+a_(13)+a_(16)=114` then `a_(1)+a_(5)+a_(12)+a_(16)` is equal to

A

64

B

76

C

98

D

38

Text Solution

Verified by Experts

The correct Answer is:
B
Key Idea Use nth term of an AP i.e. `a_(n) = a + (n-1)d`, simplify the given equations and use result
Given AP is `a_(1), a_(2), a_(3) ,.., a_(n)`
Let the above AP has common difference 'd', then `a_(1) + a_(4) + a_(7) + ...+ a_(16)`
`= a_(1) + (a_(1) + 3d) + (a_(1) + 6d) + ...+ (a_(1) + 15d)`
`= 6a_(1) + (3 + 6 + 9 + 12 + 15) d`
`:. 6a_(1) + 45d = 114` (given)
`rArr 2a_(1) + 15d = 38` ...(i)
Now, `a_(1) + a_(6) + a_(11) + a_(16)`
`= a_(1) + (a_(1) + 5d) + (a_(1) + 10d) + (a_(1) + 15d)`
`= 4a_(1) + 30d = 2(2a_(1) + 15d)`
`2 xx 38 = 76` [from Eq. (i)]
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