Question

in an AP, sum of first n term is 3n sq./2 + 5n/2. what is the 25th term?​

Answer 1

$\bf{\large{Answer}}$

Let the sum of n terms be given by Sn

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.