# How do you write the first five terms of the arithmetic sequence given a_1=5, d=6?

Sep 24, 2017

See a solution process below:

#### Explanation:

The arithmetic sequence formula is:

a_n = a_1 + (n – 1)d Where:

${a}_{n}$ is the nth term in the sequence

${a}_{1}$ is the first term in the sequence

$n$ is the term you are solving for

$d$ is the common difference for any pair of consecutive numbers in the sequence.

First Term or $n = 1$:

This is given in the problem.

${a}_{1} = 5$

Second Term or $n = 2$:

Substitute $2$ for $n$ in the formula and substitute the values from the problem giving:

a_2 = 5 + ((2 – 1) xx 6)

${a}_{2} = 5 + \left(1 \times 6\right)$

${a}_{2} = 5 + 6$

${a}_{2} = 11$

Fifth Term or $n = 5$:

Substitute $5$ for $n$ in the formula and substitute the values from the problem giving:

a_5 = 5 + ((5 – 1) xx 6)

${a}_{5} = 5 + \left(4 \times 6\right)$

${a}_{2} = 5 + 24$

${a}_{2} = 29$

Using this same process you should be able to determiner the
Third Term or $n = 3$: and Fourth Term or $n = 4$: