Question

Find the number of terms of the series 1/81,-1/27,1/9........-729.

Answer 1

Given :   1/81,-1/27,1/9........ 729.

To Find :  number of terms of the series

Solution:

1/81,-1/27,1/9........ 729.

Given series is an GP

a = 1/81

r  = (-1/27)/( 1/81)  =  - 3

nth term of GP  = arⁿ⁻¹

729  = (1/81)(-3)ⁿ⁻¹

=>   729 x 81  = (-3)ⁿ⁻¹

=>   (3)⁶ * 3⁴  = (-1)ⁿ⁻¹ 3ⁿ⁻¹

=> 3¹⁰ = (-1)ⁿ⁻¹ 3ⁿ⁻¹

=> n - 1 = 10

=> n = 11

number of terms of the series = 11

Learn More:

if x+9,x-6,4are the first three element of g.p then xis​ - Brainly.in

https://brainly.in/question/12559861

If the gp 162,54,18,...and 2/81,2/27,...have their nth terms equal then ...

https://brainly.in/question/8557652

Answer 2

Answer:

term would be like this => 11

$\huge{\orange{\overbrace{ \red{ \overbrace{\red{\underbrace \color{blue} {\underbrace \color{black} {\fcolorbox{magenta}{lime}{\fcolorbox{red}{black}{\fcolorbox{pink}{pink}{ \fcolorbox{blue}{blue}{{\bf{{{{\pink{AnSwEr}}}}}}}}}}}}}}}}}}$