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Question

The sum of 10 terms of the series 1.3.5+3.5.7+5.7.9+ is

A
28720
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B
28780
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C
28700
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D
28680
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Solution

The correct option is D 28680
The nth term is (2n1)(2n+1)(2n+3)
Tn=(2n1)(2n+1)(2n+3)
Tn=18(2n1)(2n+1)(2n+3){(2n+5)(2n3)}
=18(VnVn1) Where Vn=(2n1)(2n+1)(2n+3)(2n+5)
Sn=Tn=18[VnV0]
Sn=(2n1)(2n+1)(2n+3)(2n+5)8+158=n(2n3+8n2+7n2)
S10=28680

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