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Question

Find the nth term and the sum of n terms of the series 8,26,54,92,140,198,....

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Solution

$To find the nth term of the sequence we have to look upon the sucessive difference of the series
8,26,54,92,140.....18,28,38,48.....10,10,10.....
Let un=A+Bn+Cn2
For n=1 u1=8
A+B+C=8.....(i)
For n=2 u2=26
A+2B+4C=26.....(ii)
For n=3 u3=54
A+3B+9C=54.....(ii)
Solving (i),(ii) and (iii)
A=0,B=3,C=5
un=3n+5n2
Sn=unSn=3n+5n2Sn=3[n(n+1)2]+5[n(n+1)(2n+1)6]Sn=n(n+1)(5n+7)3


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