Question

given the sum n terms of an ap is (3n^2/ + 13/2) .find the 25th term.

Answer 1

sn=3n^2+13/2
an=sn-sn-1
=3n^2+13/2-[3(n-1)^2+13/2]
=6n^2+13/2-[3(n^2+1-2n)+13/2
=6n^2+13/2-(3n^2+3-6n)+13/2
=6n^2+13/2-(6n^2+6-12n+13/2)
=6n^2+13/2-(6n^2-12n+19/2)
=6n^2+13-6n^2+12n-19/2
=-6+12n/2
=2(-3+6n)/2
=6n-3
so ap is a1=6*1-3=3
a2=6*2-3=9....
so d=9-3=6
so 25th term=a+24d
=3+24*6
=147 ans.
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