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Question

Given a3=15,S10=125, Find d and a10

A
18
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B
4
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C
8
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D
6
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Solution

The correct option is D 8
As we know that the nth term, an=a+(n1)d
& Sum of first n terms, Sn=n2(2a+(n1)d), where a & d are the first term & common difference of an AP.
S10=125=102(2a+9d)
2a+9d=25 ............... (i)
a3=a+2d=15 ............. (ii)
Subtracting equation (ii) from (i) we get
a+7d=10 (the 8th term)
Subtracting 3rd term from 8th term we get
(a+7d)(a+2d)=1015=5
5d=5
d=1
So, a=17
a10=179=8

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