Balbharti Maharashtra State Board 11th Maths Book Solutions Pdf Chapter 2 Sequences and Series Ex 2.5 Questions and Answers.

## Maharashtra State Board 11th Maths Solutions Chapter 2 Sequences and Series Ex 2.5

Question 1.

Find Sn of the following arithmetico-geometric sequences.

(i) 2, 4x, 6x^{2}, 8x^{3}, 10x^{4}, ……

Solution:

2, 4x, 6x^{2}, 8x^{3}, 10x^{4}, ……

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

(ii) 1, 4x, 7x^{2}, 10x^{3}, 13x^{4}, ……

Solution:

1, 4x, 7x^{2}, 10x^{3}, 13x^{4}, ……

Here, 1, 4, 7, 10, 13,… are in A.P.

a = 1, d = 3

∴ nth term = a + (n – 1)d

= 1 + (n – 1)(3)

= 3n – 2

Also, 1, x, x^{2}, x^{3},… are in G.P.

∴ a = 1, r = x,

nth term = ar^{n-1} = x^{n-1}

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 = ar^{n-1} = 3 . (2^{n-1})

∴ nth term of arithmetico-geometric sequence is

Question 2.

Find the sum to infinity of the following arithmetico-geometric sequence.

(i) \(1, \frac{2}{4}, \frac{3}{16}, \frac{4}{64}, \ldots\)

Solution:

(ii) \(3, \frac{6}{5}, \frac{9}{25}, \frac{12}{125}, \frac{15}{625}, \ldots\)

Solution:

∴ \(\frac{4}{5} S=\frac{15}{4}\)

∴ S = \(\frac{75}{16}\)

(iii) \(1, \frac{-4}{3}, \frac{7}{9}, \frac{-10}{27} \ldots\)

Solution: