# How do you find the formula for a_n for the arithmetic sequence a_1=1, d=3?

Dec 11, 2017

${a}_{n} = 3 n - 2$

#### Explanation:

a generalised AP is given by

$a , a + d , a + 2 d , \ldots . a + \left(n - 1\right) d$

in this case we have

${a}_{1} = 1 , d = 3$

so

${a}_{n} = 1 + 3 \left(n - 1\right) = 1 + 3 n - 3$

${a}_{n} = 3 n - 2$

Dec 11, 2017

${a}_{n} = 3 n - 2$

#### Explanation:

$\text{the nth term of an arithmetic sequence is }$

•color(white)(x)a_n=a+(n-1)d

$\text{where a is the first term and d the common difference}$

$\text{here "a=1" and } d = 3$

$\Rightarrow {a}_{n} = 1 + 3 \left(n - 1\right) = 3 n - 2$