How do you find a formula for the nth term of this arithmetic sequence: 15, 27, 39...?

Aug 16, 2015

${a}_{n} = 3 + 12 n$

Explanation:

The sequence is
$15 , 27 , 39$

The first term:
color(blue)(a_1=15

The common difference of this sequence :
color(blue)(d=27-15=12

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

So ${a}_{n}$ for this sequence will be :
a_n=color(blue)(15)+(n-1)color(blue)(12
${a}_{n} = \left(15\right) + 12 n - 12$
${a}_{n} = 3 + 12 n$