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Question

Let Sn=(1)(5)+(2)(52)+(3)(53)+...+(n)(5n)=116[(4n1)5a+b], then

A
a=n+1
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B
a=n
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C
b=5
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D
b=25
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Solution

The correct options are
A a=n+1
C b=5
Sn=(1)(5)+(2)(52)++(n)5n.............. {i}
5Sn=(1)(5)2+(2)(53)++(n1)5n+(n)5n+1............... {ii}
Subtracting {ii} from {i} by shifting one place, we obtain
4Sn=5+52++5nn5n+1=5(5n1)4n5n+1
Sn=116[(n1)5n+1+5]
On comparing we get a=n+1 and b=5

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