Question

Sum of first n terms of an AP is 5n^2 - 3n . Find the AP and also find its 16th term.

Answer 1

Sn = 5n² - 3n

Now , sum of n terms of an A.P. = n[2a+(n-1)d]/2
⇒ an + n²d/2 - nd/2  = n(a-d/2) + n²d/2

Comparing with question fetches : d = 10  ,  a-d/2 = -3 ⇒ a = 2

So A.P. : 2 , 12 , 22, 32,...........

a₁₆ = a +15d = 2 + 15x 10 = 152

Hope this assists.