One of the most important and exam oriented question from arithmetic progression chapter as it was already asked in previous year paper of 2005 in which we have to find the nth term if the sum of the first n terms of an AP is given by Sn=(3n2−n).
Book – RS Aggarwal, Class 10, chapter 5C, question no 5
We know, nth term an=a+(n−1)d
Where
a= First term
d= Common difference
n= number of terms
an=nth term
Given,
Sn=3n2−n
S1=3(1)2−1=3−1=2
S2=3(2)2−2=12−2=10
a1=2
a2=S2−S1=10−2=8
an=a+(n−1)d
=2+(n−1)×6
=2+6n−6
=6n−4.