If sum of n terms of an AP is 2n^2+5n, then find its nth term?

Sum of first n terms of AP, S_n = 2n² + 5n

 

Now choose n =1 and put in the above formula,

First term = 2+5 = 7

 

Now put n=2 to get the sum of first two terms = 2x4 + 5x 2= 8 + 10 = 18

 

This means 

 

first term + second term = 18

 

but first term =7 as calculated above

 

so, second term = 18-7 = 11

 

So common difference becomes, 11-7 = 4

 

So the AP becomes, 7, 11, 15, ....

nth term = a + (n - 1)d = 7 + (n-1)4 = 7 + 4n - 4 = 3 + 4n