(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
(ii) a = √2, r = √2 Solution
(ii) a = √2, r = √2 Solution
(3) In a G.P. 729, 243, 81,… find t_{7} . 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.
(i) 4, 8, 16,…,8192 ? Solution
(ii) 1/3, 1/9, 1/27,................1/2187 Solution
(6) In a G.P. the 9^{th} term is 32805 and 6^{th} term is 1215. Find the 12^{th} term. Solution
(7) Find the 10^{th} term of a G.P. whose 8^{th} term is 768 and the common ratio is 2. Solution
(8) If a, b, c are in A.P. then show that 3^{a}, 3^{b}, 3^{c} are in G.P. Solution
(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 x^{b−c} × y^{c−a} × z^{a−b} = 1. Solution
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