Question

write down the nth term of each of the following G.Ps whose first terms are given as follows. Also find the term stated besides each G.P:
(I)12,-3b,........sixth term?
(ii)3,-1/3,..........;8th term?
pls anwer the both ques seperate

Answer 1

Write down the nth term of each of the following G.Ps whose first terms are given as follows. Also find the term stated besides each G.P:

(I)12,-3b,........sixth term?

(ii)3,-1/3,..........;8th term?

pls anwer the both ques seperate

$\textbf{Given:}$

$(1)12,3b,.........$

$(2)3,\frac{-1}{3},.........$

$\textbf{To find:}$

$\text{n th terms of the given G.Ps.}$

$\textbf{Solution:}$

$(1)12,3b,.........$

$\text{Here, a=12 and r=\frac{3b}{12}=\frac{b}{4} }$

$\text{n th term}$

$t_n=a\,r^{n-1}$

$\bf\,t_n=12(\frac{b}{4})^{n-1}$

$\implies\,t_6=12(\frac{b}{4})^{6-1}$

$\implies\,t_6=12(\frac{b}{4})^5$

$\implies\,t_6=12(\frac{b^5}{4^5})$

$\implies\boxed{\bf\,t_6=3(\frac{b^5}{4^4})}$

$(2)3,\frac{-1}{3},.........$

$\text{Here, a=3 and r=\frac{-1}{9} }$

$\text{n th term}$

$t_n=a\,r^{n-1}$

$\bf\,t_n=3(\frac{-1}{9})^{n-1}$

$\implies\,t_8=3(\frac{-1}{9})^{8-1}$

$\implies\,t_8=3(\frac{-1}{9})^7$

$\implies\,t_8=3(\frac{-1}{9^7})$

$\implies\boxed{\bf\,t_8=\frac{-1}{3(9^6)}}$

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