For what values of x are the numbers − 2 7 , x , − 7 2 in G.P?

The given numbers are − 2 7 , x , − 7 2 Here, first term a 1 = − 2 7 and second term a 2 = x Third term a 3 = - 7 2 Common ratio, r = a 2 a 1 = x - 2 7 = - 7 x 2 Also, common ratio, r = a 3 a 2 r = − 7 2 x = − 7 2 x So, we have: − 7 x 2 = − 7 2 x ⇒ x 2 = − 2 × 7 − 2 × 7 = 1 ⇒ x = ± 1 .

The sum of three numbers in G.P is 39 10 and their product is 1 . Find the numbers.

Let a r , a , a r be the first three terms of G.P Given: a r + a + a r = 39 10 . . . 1 and a r ( a ) ( a r ) = 1 . . . 2 From 2 , a 3 = 1 ⇒ a = 1 (Considering only real roots.) Put a = 1 in 1 , we get: 1 r + 1 + r = 39 10 ⇒ 1 + r + r 2 = 39 10 r ⇒ 10 + 10 r + 10 r 2 − 39 r = 0 ⇒ 10 r 2 − 29 r + 10 = 0 ⇒ 10 r 2 − 25 r − 4 r + 10 = 0 ⇒ 5 r ( 2 r − 5 ) − 2 ( 2 r − 5 ) = 0 ⇒ ( 5 r − 2 ) ( 2 r − 5 ) = 0 ⇒ r = 2 5 or 5 2 Corresponding term of G.P when r = 2 5 are: 5 2 , 1 , 2 5 Corresponding term of G.P when r = 5 2 are: 2 5 , 1 , 5 2 .

E M B I B E

WBCHSE Mathematics for Class 11>Algebra>Chapter 9 - Sequence and Series>EXERCISE 7F

R S Aggarwal Solutions for Exercise 6: EXERCISE 7F

Author:R S Aggarwal

R S Aggarwal Mathematics Solutions for Exercise - R S Aggarwal Solutions for Exercise 6: EXERCISE 7F

Attempt the practice questions from Exercise 6: EXERCISE 7F with hints and solutions to strengthen your understanding. WBCHSE Mathematics for Class 11 solutions are prepared by Experienced Embibe Experts.