the sum of the first n terms of an ap is (3n2/2+5n/2).find its n th term and 25th term
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Step-by-step explanation:
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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 = S2 - a1
=> a2 = 11-4 = 7
Now common difference (d)
= a2-a1 => 7-4 = 3
we know
an = a+(n-1) d
so
a25 = 4 + (25-1)(3)
=> a25 = 4 + 24×3 =>4+ 72
so 25th term of the AP is 76
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