+0

Hi good people!,

0
294
8

Hi good people!,

How do I go about finding the general term for the following sequence:

$${1\over3};{8\over9};1;{64\over81}$$

I have tested the sequence for Arithmetic, Geometric and Quadratic...but cannot determine which...please help...

Jul 25, 2018

#1
+1

Try the following:

$$1^3\frac{1}{3}; 2^3\frac{1}{3}^2;3^3\frac{1}{3}^3;4^3\frac{1}{3}^4;...etc$$

.
Jul 25, 2018
#5
0

Hi Alan,

thanx, I'll sit with it a bit to try and understand what you did...thanx a lot..

Guest Jul 25, 2018
#5
0

Hi Alan,

thanx, I'll sit with it a bit to try and understand what you did...thanx a lot..

Guest Jul 25, 2018
#2
+1

Hi good people!,
How do I go about finding the general term for the following sequence:
{1\over3};{8\over9};1;{64\over81}

$$\displaystyle {1\over3};{8\over9};1;{64\over81}$$

$$\huge{ \begin{array}{|rcll|} \hline a_1 &=& {1\over3} \\\\ a_2 &=& {8\over9} \\\\ a_3 &=& 1 \\\\ a_4 &=& {64\over81} \\\\ \ldots \\\\ a_n &=& \dfrac{n^3}{3^n} \\ \hline \end{array} }$$ Jul 25, 2018
#3
0

Hi Heureka,

I have no idea why the answer is what you say it is...How you get to it....thanx anyways...

Guest Jul 25, 2018
#3
0

Hi Heureka,

I have no idea why the answer is what you say it is...How you get to it....thanx anyways...

Guest Jul 25, 2018
#7
+1

I have no idea why the answer is what you say it is...How you get to it....thanx anyways...

$$\huge{ \begin{array}{|lrlrlrlrlrl|} \hline & a_{\color{red}1} &;& a_{\color{red}2}&;& a_{\color{red}3} &;& a_{\color{red}4} &;& \ldots &;& a_{\color{red}n} \\ \hline & \dfrac{1}{3}&;& \dfrac{8}{9}&;& 1&;& \dfrac{64}{81}&;& \ldots &;& \\\\ \Rightarrow & \dfrac{1^1}{3^1}&;& \dfrac{2^3}{3^2}&;& 1&;& \dfrac{4^3}{3^4}&;& \ldots &;& \\\\ \Rightarrow & \dfrac{{\color{red}1}^1}{3^{\color{red}1}}&;& \dfrac{{\color{red}2}^3}{3^{\color{red}2}}&; & \dfrac{{\color{red}3}^3}{3^{\color{red}3}}&;& \dfrac{{\color{red}4}^3}{3^{\color{red}4}}&;& \ldots &;&\dfrac{{\color{red}n}^3}{3^{\color{red}n}} \\ \hline \end{array} }$$ heureka  Jul 25, 2018
edited by heureka  Jul 25, 2018
#8
+2

Heureka,

thank you kindly...makes sooo much sense!!!.. juriemagic  Jul 25, 2018