GEOMETRIC SEQUENCE WORKSHEET FOR GRADE 10

(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 t₇ .     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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