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Question

# Consider a sequence whose sum to n terms is given by the quadratic function Sn=3n2+5n The nature of the given series is

A
A.P
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B
G.P
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C
H.P
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D
AGP
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Solution

## The correct option is B A.PTo convert from Sn to Tn we can write Tn=Sn−Sn−1Shortcut Method: If Sn is quadratic in n then:Replace n2 by (2n−1) and n by 1.Using Shortcut method:Tn=3(2n−1)+5(1) =6n−2+5=6n+3Thus, Tn=6n+2To check the nature of the series let us check the Tn for the values n=1,2,3,.T1=6×1+2=6+2=8T2=6×2+2=12+2=14T3=6×3+2=18+2=20Thus the sequence is 8,14,20,.. whose first term is 8 and the common difference is 14−8=20−14=6Hence, the nature of the given series is in A.P

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