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Question

# If the ratio of sum of first n terms of two A.P.s is 2n+8:5n−3, then the ratio of nth terms of those two A.P.s is

A
2n+5:5n+1
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B
2n+3:5n4
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C
2n+18:5n1
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D
2n+18:5n+1
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Solution

## The correct option is B 2n+3:5n−4Let, for 1st A.P., first term =a1 and common difference =d1 and, for 2nd A.P., first term =a2 and common difference =d2 (Sn)1(Sn)2=2n+85n−3 ⇒n2[2a1+(n−1)d1]n2[2a2+(n−1)d2]=2n+85n−3 ⇒2a1+(n−1)d12a2+(n−1)d2=2n+85n−3 Replacing n with (2n−1) in above equation, we get 2a1+(2n−2)d12a2+(2n−2)d2=4n+610n−8 ⇒a1+(n−1)d1a2+(n−1)d2=2n+35n−4 ∴(tn)1(tn)2=2n+35n−4

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