Question

How do I solve this?
What is the 9th term of this geometric sequence?

2/3, 2, 6, 18, 54, 162, ...

Answer 1

well.... what's "r" or the common ratio?
or
what makes a geometric sequence a geometric sequence?

Answer 2

Umm.. what it is multiplied by? Isn't it like squares or something... I'm sorry I'm really bad at this stuff :(

Answer 3

let us make a sequence
lemme start with the 1st term say 11
and use the common ratio "r" of.. say 2

if 11 is the first term, what's the 2nd term?

Answer 4

22?

Answer 5

yeap... so... notice \(\begin{array}{llll}
term&value
\\\hline\\
a_1&11\\
a_2&a_1\cdot r\implies 11\cdot 2\implies 22
\end{array}\qquad meaning\qquad a_2=a_1\cdot r\qquad thus
\\ \quad \\\\ \quad \\
\cfrac{a_2}{a_1}=r\qquad or\qquad \cfrac{\cancel{22}}{\cancel{11}}=r\implies 2=r\)

Answer 6

so.. to find "r", simply divide the "following term" by the term behind it :)

Answer 7

Oh! Awesome that is much easier than I thought thank you so much!

Answer 8

to find the 9th term, well \(\bf \large a_{\color{brown}{ n}}=a_1\cdot r^{{\color{brown}{ n}}-1}\qquad \qquad a_{\color{brown}{ 9}}=a_1\cdot r^{{\color{brown}{ 9}}-1}\)

Answer 9

so I got 4,374