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 D28680 The nth term is (2n−1)(2n+1)(2n+3) Tn=(2n−1)(2n+1)(2n+3) Tn=18(2n−1)(2n+1)(2n+3){(2n+5)−(2n−3)} =18(Vn−Vn−1)WhereVn=(2n−1)(2n+1)(2n+3)(2n+5) Sn=∑Tn=18[Vn−V0] ⇒Sn=(2n−1)(2n+1)(2n+3)(2n+5)8+158=n(2n3+8n2+7n−2) ∴S10=28680