Is the series 3 + 33 + 333 + … a Geometric series?

The given series is: 3 + 33 + 333 + … To check the given series is G.P. or not, find the common ratio r Any series with a fixed common ratio is a G.P. The common ratio of a series is the ratio of its consecutive terms So, r 1 = 33 3 = 11 and r 2 = 333 33 = 10 . 09 We see, the common ratios r 1 ≠ r 2 Hence, the given series is not a G.P.

Find the value of r , such that 1 + r + r 2 + r 3 … = 3 4 .

The given series is: 1 + r + r 2 + r 3 … = 3 4 . This is an infinite series with a = 1 . We know that the sum to infinite number of terms of a G.P. is = a 1 - r , - 1 < r < 1 . Therefore, we get, 3 4 = a 1 - r = 1 1 - r ⇒ 4 = 3 - 3 r ⇒ 3 r = 3 - 4 ⇒ 3 r = - 1 ⇒ r = - 1 3 Therefore, the required value of r is - 1 3 .

E M B I B E

Mathematics Standard 10>Chapter 2 - Numbers And Sequences>Progress Check

Progress Check

Author:Tamil Nadu Board

Tamil Nadu Board Mathematics Solutions for Exercise - Progress Check

Simple step-by-step solutions to Progress Check questions of Numbers And Sequences from Mathematics Standard 10. Also get 3D topic explainers, cheat sheets, and unlimited doubts solving on EMBIBE.