  ### Home > CCG > Chapter 5 > Lesson 5.1.4 > Problem5-43

5-43.

Write an equation for each sequence.

1. $108$, $120$, $132$, $\dots$

A recursive formula specifies the first term, then gives a formula for each 'next term' based on the previous term.

Identify the first term and common difference in the sequence.

$a_1=\text{starting value}$; $a_n=a_{n-1}+d$, where $a_{n-1}$ stands for previous term and $d$ stands for the difference in the sequence.

$a_1=108$; $a_n=a_{n-1}+12$

1. $\frac { 2 } { 5 }$, $\frac { 4 } { 5 }$, $\frac { 8 } { 5 }$, $\dots$

Find the pattern in the sequence. What do you have to multiply by in order to get to the next term?

$a_1=\text{starting value}$; $a_n=(a_{n-1})(r)$, where $a_{n-1}$ stands for the previous term and "$r$" stands for the the common ratio (multiplier) in the sequence

$a_1=\frac{2}{5}$$a_n=(a_{n-1})(2)$

1. $3741$, $3702$, $3663$, $\dots$

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.

$a(n)=39(n-1)+3741$

1. $117$, $23.4$, $4.68$, $\dots$

Find the common ratio (multiplier) in the sequence.

Use the equation for geometric sequences:

$a_n=a_1·r^{n-1}$

$a_n=117(0.2)^{n-1}=585(0.2)^n$