Question

in an AP the sum of first n terms is 3n^2/2 + 5n/2 find the 25th term.

Answer 1

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.

Answer 2

Hey hi !!

Sn = 3n²/2 + 5n/2

We know that ,

nth term = (sum of nth term) - (sum of (n-1)th term)

So , according to the question ,

25th term = (sum of 25th term) - (sum of (25-1)th term)
= (sum of 25th term) - (sum of 24th term)
= [3(25)²/2 + 5(25)/2] - [3(24)²/2 + 5(24)/2]
= [1875/2 + 125/2] - [1728/2 + 120/2]
= (2000/2) - (864 + 60)
= 1000 - 924
= 76

So , the 25th term of the AP is 76.

Hope it helps !