a)For the sequence $2,4,8,16,32,...$, what number is multiplied each time to get the next term?
b)Find a formula for the general term, $u_n$ of $2,4,8,16,32,...$
Write your answer in the form $b^n$
c)Find a formula for the general term, $u_n$ of $1,2,4,8,16,32,...$
Write your answer in the form $b^{n-1}$
d)Find a formula for the general term, $u_n$ of $3,6,12,24,48,96,...$
Write your answer in the form $a\left(b\right)^{n-1}$
e)Find a formula for the general term, $u_n$ of $6,12,24,48,96,...$
Write your answer in the form $a\left(b\right)^{n-1}$
f)Find a formula for the general term, $u_n$ of $-1,-2,-4,-8,-16,-32...$
Write your answer in the form $b^{n-1}$
g)Find a formula for the general term, $u_n$ of $1,-2,4,-8,16,-32...$
Write your answer in the form $(b)^{n-1}$
h)Find a formula for the general term, $u_n$ of $-3,6,-12,24,-48,96,...$
Write your answer in the form $a\left(b\right)^{n-1}$
Terms of Geometric Sequences
Find the first 5 terms for each geometric sequence.
Write the terms separated by commas.
For example,
Question:
$u_n=5^n$
Answer:
$5,25,125,625,3125$
a)$u_n=3^n$
b)$u_n=3^{n-1}$
c)$u_n=2\left(3\right)^{n-1}$
d)$u_n=-2\left(3\right)^{n-1}$
e)$u_n=2\left(-3\right)^{n-1}$
f)$u_n=-2\left(-3\right)^{n-1}$
The $n^{th}$ Term of a Geometric Sequence
For geometric sequences, the number that is multiplied each time to find the next term is called the
.
It is usually denoted by the letter
.
$$u_1\overset{\times r}{\overset{\Huge\frown}{\phantom{A},\phantom{B}}}\underset{u_2}{\text{___}}\overset{\times r}{\overset{\Huge\frown}{\phantom{A},\phantom{B}}}\underset{u_3}{\text{___}}\overset{\times r}{\overset{\Huge\frown}{\phantom{A},\phantom{B}}}\underset{u_4}{\text{___}}\overset{\times r}{\overset{\Huge\frown}{\phantom{A},\phantom{B}}}\underset{u_5}{\text{___}}\phantom{A},\quad\ldots$$
Let's find the terms of a geometric sequence starting from $u_1$:
$\qquad u_2 = u_1 r$
$\qquad u_3 = u_1 r^2$
$\qquad u_4 = u_1 r^3$
Follow this pattern and express $u_5$ and $u_6$ in terms of $u_1$ and $r$
$\qquad u_5 = $
$\qquad u_6 = $
To find $u_n$, how many $r$'s must be multiplied to $u_1$?
For geometric sequences, $u_n=$
.
General Term of Geometric Sequences
Find the general term, $u_n$, for the following sequences.
*Write your answers in the form $b^{n-1}$ or $\left(b\right)^{n-1}$ or $a\left(b\right)^{n-1}$ or $a\left(\frac{b}{c}\right)^{n-1}$ where $a,b,c$ are numbers.