Question

in an A.P., the sum of first n terms is given bySn=3n 2 /2+5n/2. Find the 25th term of the A.P.

Answer 1

sn= 3n^2/2+5n/2
s1=3*1/2 +5*1/2 =3/2+5/2=8/2=4

s2= 3*2^2/2+5*2/2 =6+5=11

s3=3*3^2/2 +5*3/2=27/2+15/2=42/2=21

first term=a=a1= s1=4
a2=s2-s1=11-4=7

a3= s3-s2=21-11=10

common difference= d=a2-a1=7-4=3
n th term =an= a+(n-1)d
a25=4+(25-1)3
=4+24*3
=4+72
=76