**Question 1.Find Sn of the following arithmetico-geometric sequences.**

Here, 2, 4, 6, 8, 10,… are in A.P.

∴ a = 2, d = 2

∴ nth term = a + (n – 1)d

= 2 + (n – 1)(2)

= 2n

nth term of arithmetico-geometric sequence is

**(iii) 1, 2 × 3, 3 × 9, 4 × 27, 5 × 81, ……Solution:**1, 2 × 3, 3 × 9, 4 × 27, 5 × 81, …..

Here, 1, 2, 3, 4, 5, … are in A.P.

∴ a = 1, d = 1

∴ nth term = a + (n – 1)d

= 1 + (n – 1)1

= n

**(iv) 3, 12, 36, 96, 240, ……Solution:**

3, 12, 36, 96, 240, ……

i.e., 1 × 3, 2 × 6, 3 × 12, 4 × 24, 5 × 48, …….

Here, 1, 2, 3, 4, 5, ….. are in A.P.

∴ nth term = n

Also, 3, 6, 12, 24, 48, ….. are in G.P.

∴ a = 3, r = 2

∴ nth term = = 3 . ()

∴ nth term of arithmetico-geometric sequence is

**Question 2.Find the sum to infinity of the following arithmetico-geometric sequence.Solution:**

Solution:

Solution: