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(26C) Geometric sequences

Exploring Geometric Sequences

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) $u_n=-2\left(-3\right)^{n-1}$

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.

a) $2,6,18,54,...$

b) $10,50,250,1250...$

c) $1,-3,9,-27,...$

d) $32,16,8,4,2,...$

e) $12,18,27,\frac{81}{2},...$

f) $\frac{1}{16},\frac{1}{8},\frac{1}{4},\frac{1}{2},...$

g) $-64,16,-4,1,-\frac{1}{4},...$

Exercises

(26C on P.538) #1-2 odd letters