Question

If the sum of first n terms of an AP is given by Sn=2n^2-5n,finf its nth term

Answer 1

Sum of first n terms of an AP => Sn=2n^2-5
Now put n=1 and put in the above formula
First term = 2(1)^2-5(1) =2-5=-3
Now put n=2 to get the sum of first two terms=2(2)^2-5(2)=8-10=-2
This means
First term + Second term=-2
-3+ Second term=-2
Second term = -2+3 = 1
Common Difference = 1-(-3)=1+3=4
AP becomes -3,1,5......
nth term=a+(n-1)d
= -3+(n-1)4
= -3+4n-4
= 4n-7