# Given the first term and the common dimerence er an arithmetic sequence how do you find the 52nd term and the explicit formula: a_1=37, d=200?

Jul 10, 2017

${a}_{52} = 10237 \text{ and } {a}_{n} = 200 n - 163$

#### Explanation:

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

•color(white)(x)a_n=a_1+(n-1)d

$\Rightarrow {a}_{52} = 37 + \left(51 \times 200\right) = 10237$

$\text{the general ( explicit) formula}$

${a}_{n} = 37 + 200 \left(n - 1\right)$

$\textcolor{w h i t e}{{a}_{n}} = 37 + 200 n - 200$

$\Rightarrow {a}_{n} = 200 n - 163$