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Question

Let a1,a2,,a30 be in A.P., S=30i=1ai and T=15i=1a2i1. If a5=27 and S2T=75, then the value of a10 is

A
47
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B
52
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C
42
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D
57
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Solution

The correct option is B 52
Let d be the common difference of A.P.
S=a1+a2++a30 =302[2a1+29d]=15[2a1+29d]
T=a1+a3++a29 =152[2a1+14(2d)]=15[a1+14d]

Given that S2T=75
15d=75d=5
Also given that a5=27
a1+4d=27a1=7
Hence, a10=a1+9d=52

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