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Question

Let Sn denotes the sum of the first n terms of an A.P.. If S4=16 and S6=48, then S10 is equal to

A
260
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B
320
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C
380
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D
410
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Solution

The correct option is B 320
Let a be the first term and d is common difference of the A.P.
Given, S4=42(2a+3d)=16
2a+3d=8 (1)

and S6=62(2a+5d)=48
2a+5d=16 (2)

Solving (1) and (2), we get
a=22 and d=12

S10=102(2a+9d)=10×22+45×(12)
S10=320


Alternate Approach––––––––––––––––––––
S6S4=a5+a6=4816=64

If there are 10 terms in an A.P., then the mean of the 10 terms is given by=a5+a62=32
Therefore, Sum S10=32×10=320

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