CPM Homework Help : CCG Problem 5-43

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Home > CCG > Chapter 5 > Lesson 5.1.4 > Problem 5-43

5-43.

Write an equation for each sequence.

$108$ , $120$ , $132$ , $\dots$
Hint 1(a):
A recursive formula specifies the first term, then gives a formula for each 'next term' based on the previous term.
Hint 2(a):
Identify the first term and common difference in the sequence.
Step (a):
$a_1=\text{starting value}$ ; $a_n=a_{n-1}+d$ , where $a_{n-1}$ stands for previous term and $d$ stands for the difference in the sequence.
Answer (a):
$a_1=108$ ; $a_n=a_{n-1}+12$

$\frac { 2 } { 5 }$ , $\frac { 4 } { 5 }$ , $\frac { 8 } { 5 }$ , $\dots$
Hint (b):
Find the pattern in the sequence. What do you have to multiply by in order to get to the next term?
Step (b):
$a_1=\text{starting value}$ ; $a_n=(a_{n-1})(r)$ , where $a_{n-1}$ stands for the previous term and " $r$ " stands for the the common ratio (multiplier) in the sequence
Answer (b):
$a_1=\frac{2}{5}$ ; $a_n=(a_{n-1})(2)$

$3741$ , $3702$ , $3663$ , $\dots$
Hint (c):
The general equation for an arithmetic sequence is $a(n)=d(n-1)+a_1$ , where $n=\text{position}$ in the sequence, $d$ is the difference, and $a_1$ is the starting value.
Answer (c):
$a(n)=39(n-1)+3741$

$117$ , $23.4$ , $4.68$ , $\dots$
Hint (d):
Find the common ratio (multiplier) in the sequence.
Step (d):
Use the equation for geometric sequences:
$a_n=a_1·r^{n-1}$
Answer (d):
$a_n=117(0.2)^{n-1}=585(0.2)^n$

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