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Question

the sum of the first n terms of an AP is (5n22+3n2). Find the nth term and the 20th term of this AP.

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Solution

Sum of n terms, Sn=5n22+3n2

S1=5(1)22+3(1)2=52+32=82=4=a

S1=5(2)22+3(2)2=202+62=10+3=13

a2=S2S1=134=9

d=a2a1=94=5

an=a+(n1)d=4+(n1)5=4+5n5=5n1

a20=5n1=5×201=1001=99


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