KC Sinha Mathematics Solution Class 11 Chapter 18 Geometric Progressions Exercise 18.1

 Exercise 18.1

Page no 18.8

Type 1

Question 1

Find the 10 th term of the G.P. $5,25,125, \ldots .$ Also find its nth term.

Question 2

Find the 8 th term of the G.P. $0.3,0.06,0.012, \ldots$

Question 3

Find the 20 th and $n$th term of the G.P. $\frac{5}{2}, \frac{5}{4}, \frac{5}{8}, \ldots$

Question 4

Find the 12 th term of a G.P. whose 8 th term is 192 and common ratio  2

Question 5

Which term of the geometric sequence:

(i) $2 \sqrt{3}, 6,6 \sqrt{3}, \ldots$ is 1458 ?

(ii) $\sqrt{3}, 3,3 \sqrt{3}, \ldots$ is 729 ?

(iii) $2,8,32, \ldots$ is 131072 ?

(iv) $0.004,0.02,0.1, \ldots$ is $12.5 ?$

(v) $\frac{1}{3}, \frac{1}{9}, \frac{1}{27}, \ldots$ is $\frac{1}{19683}$ ?

(vi) $\frac{1}{4},-\frac{1}{2}, 1,-2, \ldots$ is $64 ?$

Question 5

Which term of the geometric sequence:

(i) $2 \sqrt{3}, 6,6 \sqrt{3}, \ldots$ is 1458 ?

(ii) $\sqrt{3}, 3,3 \sqrt{3}, \ldots$ is 729 ?

(iii) $2,8,32, \ldots$ is 131072 ?

(iv) $0.004,0.02,0.1, \ldots$ is $12.5$ ?

(v) $\frac{1}{3}, \frac{1}{9}, \frac{1}{27}, \ldots$ is $\frac{1}{19683}$ ?

(vi) $\frac{1}{4},-\frac{1}{2}, 1,-2, \ldots$ is $64 ?$

Question 6

How many terms are there in the a.P. $0.03,0.06,0.12, \ldots, 3.84$ ?

Question 7

If 5 th and 8 th terms of a GP. be 48 and 384 respectively. Find the G.P. if term of G.P. are real numbers.

Page no 18.9

Question 8

If the 6 th and 10th terms of a G.P. are $\frac{1}{16}$ and $\frac{1}{256}$ respectively. Find the GP. if

its terms are real numbers.

Question 9

If the pth. qth and r th terms of a G.P are a,b and c respectively . Prove that $a^{q-r} b^{r-p} c^{p-q}=1$

Question 10

If the 5 th, 8 th and 11 th terms of a G.P. are $p, q$ and $s$ respectively, show that $q^{2}=p s$.

Question 11

If the $4 \mathrm{th}, 10 \mathrm{th}$ and 16 th terms of a G.P. are $x, y, z$ respectively. Prove that $x, y, z$ are in G.P.

Question 12

The fourth term of the square of its second term, and the first term is -3 Determine its  7 th term.

Question 13

If the $(p+q)$ th term of a GP. is $a$ and the $(p-q)$ th term is $b$, show that its $p$ th term is $\sqrt{a b}$.

Type 2

Question 14

The product of three consecutive terms of a G.P. is $-64$ and the first term is four times the third. Find the terms.

Question 15

 Find a GP. for which the sum of the first two terms is $-4$ and the fifth term is 4 times the third.

Question 16

Find three numbers in G.P. whose sum is 13 and the sum of whose squares is 91 .

Question 17

The sum of first three terms of a G.P. is $\frac{13}{12}$ and their product is $-1$. Find the common ratio and the terms (Assume the terms of G.P. to be real numbers).

Question 18

The sum of first three terms of a G.P. is 16 and the sum of the next three terms is 128 . Determine the first term and the common ratio of the G.P.

Question 19

The first term of a G.P. is 1. The sum of the third term and fifth term is 90 . Find the common ratio of G.P.

Question 20

Three numbers whose sum is 15 are in A.P. If $1,4,19$ be added to them respectively, the resulting numbers are in G.P. Find the numbers.

[HOTS]

Question 21

The sum of three numbers in G.P. is 56. If we subtract 1, 7,21 from these numbers in that order, we obtain an A.P. Find the numbers.

Question 22

Find three numbers in G.P. whose sum is 52 and the sum of whose products in pairs is 624

Question 23

From three numbers in G.P. other three numbers in G.P. are subtracted and the remainder are also found to be in G.P. Prove that the three sequences have the same common ratio.