**Chapter 2 Sequences and Series Ex 2.2**

## Chapter 2 Sequences and Series Ex 2.2

**Question 1.For the following G.P.s, find .(i) 3, 6, 12, 24, ……..Solution:**

Solution:

**(iii) 0.7, 0.07, 0.007, …….Solution:**

**(iv) √5, -5, 5√5, -25, …….Solution:**

**Question 2.For a G.P.Solution:**

**(ii) If = 1023, r = 4, find a.Solution:**

**Question 3.For a G.P.(i) If a = 2, r = 3, = 242, find n.Solution:**

**(ii) For a G.P. sum of the first 3 terms is 125 and the sum of the next 3 terms is 27, find the value of r.Solution:**

**Question 4.For a G.P.Solution:**

Solution:

**Question 5.Find the sum to n terms(i) 3 + 33 + 333 + 3333 + …..Solution:**

**(ii) 8 + 88 + 888 + 8888 + …..Solution:**

**Question 6.Find the sum to n terms(i) 0.4 + 0.44 + 0.444 + …..Solution:**

(ii) 0.7 + 0.77 + 0.777 + ……

Solution:

**Question 7.Find the sum to n terms of the sequence(i) 0.5, 0.05, 0.005, …..Solution:**

**(ii) 0.2, 0.02, 0.002, ……Solution:**

**Question 8.For a sequence, if = 2(3n – 1), find the nth term, hence showing that the sequence is a G.P.Solution:**

**Question 9.**

**Question 10.Solution:**
Let a and r be the 1st term and common ratio of the G.P. respectively.

**Question 11.FindSolution:**

Solution:

**Question 12.The value of a house appreciates 5% per year. How much is the house worth after 6 years if its current worth is Rs. 15 Lac. [Given: (1.05 = 1.28, (1.05 = 1.34]Solution:**

The value of a house is Rs. 15 Lac.

Appreciation rate = 5% = 5/100 = 0.05

Value of house after 1st year = 15(1 + 0.05) = 15(1.05)

Value of house after 6 years = 15(1.05) (1.05

= 15(1.05

= 15(1.34)

= 20.1 lac.

**Question 13.If one invests Rs. 10,000 in a bank at a rate of interest 8% per annum, how long does it take to double the money by compound interest? [(1.08 = 1.47]Solution:**

Amount invested = Rs. 10000

Interest rate = 8/100 = 0.08

amount after 1st year = 10000(1 + 0.08) = 10000(1.08)

Value of the amount after n years

= 10000(1.08) × (1.08

= 10000(1.08

= 20000

∴ (1.08 = 2

∴ (1.08 = 1.47 …..[Given]

∴ n = 10 years, (approximately)