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Question

(i) the sum fo the first n terms of an AP is (5n22+3n2). Find hte nth term and the 20th term of this AP.
(ii) The sum of the first n terms of an AP is (3n22+5n2). Find its nth term and the 25th term.

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Solution

(i) 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

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

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

S1=3(2)22+3(2)2=122+102=6+5=11

a2=S2S1=114=7

d=a2a1=74=3

an=a+(n1)d=4+(n1)3=4+3n3=3n+1

a25=3n+1=3×25+1=75+1=76


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