(1) Which of the following sequences are in G.P.?

(i) 3, 9, 27, 81,… Solution

(ii) 4,44,444,4444,... Solution

(iii) 0.5, 0.05, 0.005,… Solution

(iv) 1/3, 1/6, 1/12,....... Solution

(v) 1, −5, 25, −125,… Solution

(vi) 120,60,30,18,… Solution

(vii) 16, 4, 1, 1/4,.......... Solution

(2) Write the first three terms of the G.P. whose first term and the common ratio are given below.

(i) a = 6, r = 3 Solution

(4) Find x so that x + 6, x + 12 and x + 15 are consecutive terms of a Geometric Progression. Solution

(5) Find the number of terms in the following G.P.

(9) In a G.P. the product of three consecutive terms is 27 and the sum of the product of two terms taken at a time is 57/2 . Find the three terms. Solution

(10) A man joined a company as Assistant Manager. The company gave him a starting salary of ₹60,000 and agreed to increase his salary 5% annually. What will be his salary after 5 years? Solution

(11) Sivamani is attending an interview for a job and the company gave two offers to him.

Offer A: ₹20,000 to start with followed by a guaranteed annual increase of 6% for the first 5 years.

Offer B: ₹22,000 to start with followed by a guaranteed annual increase of 3% for the first 5 years.

What is his salary in the 4th year with respect to the offers A and B? Solution

(12) If a, b, c are three consecutive terms of an A.P. and x, y, z are three consecutive terms of a G.P. then prove that xb−c × yc−a × za−b = 1. Solution