Question

If the sum of first n terms of an AP is given by
Sn=3n² + 2n, find the nth term of AP​

Answer 1

Answer:

6n - 1

Step-by-step explanation:

Sum of n terms of an AP S(n) = 3n² + 2n

nth term of AP a(n) = S(n) - S(n - 1)

⇒ a(n) = 3n² + 2n - [ 3( n - 1 )² + 2( n - 1 ) ]

⇒ a(n) = 3n² + 2n - [ 3( n² - 2n + 1 ) + 2n - 2 ]

⇒ a(n) = 3n² + 2n - [ 3n² - 6n + 3 + 2n - 2 ]

⇒ a(n) = 3n² + 2n - [ 3n² - 4n + 1 ]

⇒ a(n) = 3n² + 2n - 3n² + 4n - 1

⇒ a(n) = 6n - 1

Therefore the nth term of AP is 6n - 1