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Question

The value of 15+3+17+5+19+7+ upto 100 terms is

A
100203+3
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B
1002033
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C
200218+12
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D
20021812
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Solution

The correct option is A 100203+3
Let
Sn=15+3+17+5+19+7++Tn
So Tn=12n+3+2n+1,nN
Tn=2n+32n+12=12[2n+32n+1]
So,
Sn=T1+T2+T3++Tn=12[53]+12[75]+12[97]+ +12[2n+32n+1]Sn=12[2n+33]Sn=n2n+3+3S100=100203+3

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