# How do you find a formula for the nth term of each arithmetic sequence: 24,32,40,48,.......?

Aug 16, 2015

color(blue)(a_n=16 +8n ( for $n = 1 , 2 , 3 , 4. . .$)

#### Explanation:

The arithmetic sequence is
$24 , 32 , 40 , 48$

The first term color(blue)(a_1 = 24
The common difference of the sequence is
color(blue)(d=32-24=8

The $n t h$ term of an arithmetic sequence is given by formula:
color(blue)(a_n=a+(n-1)d

So for the above sequence
a_n=color(blue)(24) +(n-1)color(blue)(8
${a}_{n} = 24 + 8 n - 8$
${a}_{n} = 16 + 8 n$