The sum of first three terms of a G . P . is 13 12 and their product is - 1 . Find the G . P .

Let the first three terms of G . P . be a r , a , a r Given that a r + a + a r = 13 12 and a r a a r = - 1 a 3 = - 1 ⇒ a = - 1 a r + a + a r = 13 12 a 1 r + 1 + r = 13 12 r 2 + r + 1 = - 13 12 r 4 r + 3 3 r + 4 = 0 r = - 3 4 , - 4 3 If r = - 3 4 G . P . 4 3 , - 1 , 3 4 … Or if r = - 4 3 G . P . 3 4 , - 1 , 4 3 …

The sum of first three terms of a G . P . is 39 10 and their product is 1 . Find the common ratio and the terms.

Let three numbers of G . P . are a r , a , a r Given that a r + a + a r = 39 10 .....(i) Given: a r a a r = 1 a 3 = 1 ⇒ a = 1 Put a = 1 in equation (i) 1 r + 1 + r = 39 10 10 r 2 + r + 1 = 39 r 10 r 2 - 29 r + 10 = 0 r = 5 2 or 2 5 Required numbers are 2 5 , 1 , 5 2 or 5 2 , 1 , 2 5

E M B I B E

MATHEMATICS for CLASS XI>Chapter 20 - Geometric Progressions>EXERCISE 20.2

R D Sharma Solutions for Chapter: Geometric Progressions, Exercise 2: EXERCISE 20.2

Author:R D Sharma

R D Sharma Mathematics Solutions for Exercise - R D Sharma Solutions for Chapter: Geometric Progressions, Exercise 2: EXERCISE 20.2

Attempt the free practice questions on Chapter 20: Geometric Progressions, Exercise 2: EXERCISE 20.2 with hints and solutions to strengthen your understanding. MATHEMATICS for CLASS XI solutions are prepared by Experienced Embibe Experts.

Questions from R D Sharma Solutions for Chapter: Geometric Progressions, Exercise 2: EXERCISE 20.2 with Hints & Solutions

MEDIUM

11th CBSE

IMPORTANT

MATHEMATICS for CLASS XI>Chapter 20 - Geometric Progressions>EXERCISE 20.2>Q 2

Find three numbers in $G . P .$ whose sum is $38$ and their product is $1728$ .

MEDIUM

11th CBSE

IMPORTANT

MATHEMATICS for CLASS XI>Chapter 20 - Geometric Progressions>EXERCISE 20.2>Q 3

The sum of first three terms of a $G . P .$ is $\frac{13}{12}$ and their product is $- 1$ . Find the $G . P$ .

MEDIUM

11th CBSE

IMPORTANT

MATHEMATICS for CLASS XI>Chapter 20 - Geometric Progressions>EXERCISE 20.2>Q 4

The product of three numbers in $G . P .$ is $125$ and the sum of their products taken in pairs is $87 \frac{1}{2}$ . Find them.

EASY

11th CBSE

IMPORTANT

MATHEMATICS for CLASS XI>Chapter 20 - Geometric Progressions>EXERCISE 20.2>Q 5

The sum of first three terms of a $G . P .$ is $\frac{39}{10}$ and their product is $1$ . Find the common ratio and the terms.

MEDIUM

11th CBSE

IMPORTANT

MATHEMATICS for CLASS XI>Chapter 20 - Geometric Progressions>EXERCISE 20.2>Q 6

The sum of three numbers in $G . P .$ is $14$ . If the first two terms are each increased by $1$ and the third term decreased by $1$ , the resulting numbers are in $A . P .$ Find the numbers.