# How do you write the nth term rule for the arithmetic sequence with d=5/3 and a_8=24?

Jul 22, 2016

${a}_{n} = \frac{1}{3} \left(32 + 5 n\right)$

#### Explanation:

The ${n}^{t h}$ term of an arithmetic sequence in terms of the ${m}^{t h}$ term and the common difference $\left(d\right)$ is given by:

${a}_{n} = {a}_{m} + \left(n - m\right) d$
In this example; $m = 8 , d = \frac{5}{3}$ and ${a}_{8} = 24$

Replacing these values into the general formula above$\to$
${a}_{n} = {a}_{8} + \left(n - 8\right) \cdot \frac{5}{3}$

${a}_{n} = 24 + \left(n - 8\right) \cdot \frac{5}{3}$
$= \frac{1}{3} \left(72 + 5 n - 40\right)$

$= \frac{1}{3} \left(32 + 5 n\right)$