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If the sum of the first n terms of an A.P. is 1/2 (3n^2 +7n), then find its nth term. Hence write its 20th term. - Mathematics

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Question

If the sum of the first n terms of an A.P. is 1/2(3n2 +7n), then find its nth term. Hence write its 20th term.

Solution

Sn=1/2(3n2+7n)

S1=12(3+7)=5

S2=12(3×22+7×2)=26/2=13

We know

S1=a1=5

S2=a1+a2=13

S2S1=a1+a2a1

135=a2

a2=8

We know

d=a2a1

d=85=3

We know that the nth term of the AP is given by

an=a+(n1)d

an=5+(n1)3

an=2+3n

Thus, the nth term of the AP is 2+3n.

Thus, the 20th term is

a20=2+3(20)=62

Hence, the 20th term of the AP is 62.

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