How do you write a rule for the nth term of the arithmetic sequence given d=2, a_1=5?

Jul 18, 2016

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

Explanation:

The terms in the standard $\textcolor{b l u e}{\text{Arithmetic sequence}}$ are

$a , a + d , a + 2 d , a + 3 d , \ldots \ldots , a + \left(n - 1\right) d$

where a is the 1st term, d, the common difference and the nth term is a + (n -1)d

Each term in the sequence is obtained by adding d to the previous term.

Using the nth term, that is a + (n -1)d

with a = 5 and d = 2

$\Rightarrow {a}_{n} = 5 + 2 \left(n - 1\right) = 5 + 2 n - 2 = 2 n + 3$