Question

the sum of first n term of the ap is given by SN equals to 2n²+3n find the sixteenth term of ap

Answer 1

Sn=2n²+3n
So if n=1
we find the sum of the first one term=a
S1=2(1²)+3(1)
S1=2+3
S1=5=a

Now
if n=2
we find the sum of the first two terms=a+a2
S2=2(2)²+3(2)
S2=8+6
S2=14=a+a2
a+a2=14
5+a2=14
a2=14-5
a2=9

Now a=5 and a2=9
So
d=a2-a
d=9-5
d=4
now
an=a+(n-1)d
a16=5+(16-1)4
a16=5+60
a16=65


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