OMTEX CLASSES: NUMBERS AND SEQUENCES EX. NO. 2.7

NUMBERS AND SEQUENCES EX. NO. 2.7

2. NUMBERS AND SEQUENCES

EX. NO. 2.7

(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 = 1000, r = 2/5 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 9th term is 32805 and 6th term is 1215. Find the 12th term. Solution

(7) Find the 10th term of a G.P. whose 8th term is 768 and the common ratio is 2. Solution

(8) If a, b, c are in A.P. then show that 3a, 3b, 3c 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 xb−c × yc−a × za−b = 1. Solution