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Question

In an AP the sum of first n terms is 3n2÷2+5n÷2 then find the 25th term.

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Solution

Let the sum of n terms be given by Sn
so
Sn=3n²/2+5n/2
S1=3(1)²/2+5(1)/2
=3/2+5/2=4
So 1st term is 4 say a
Now
S2=3(2)²/2+5(2)/2
=6+5=11

Now a2=S2a1
=>a2=114=7

Now common difference (d)
=a2a1=74=3

we know , n th term of A.P. is given as,
an=a+(n1)d
So ,
a25=4+(251)(3)
a25=4+24×3=4+72
Hence, 25th term of the AP is 76


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