# 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=25, d=6?

Nov 20, 2017

${a}_{n} = 6 n + 19 \text{ and } {a}_{52} = 331$

#### Explanation:

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

•color(white)(x)a_n=a+(n-1)d

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

$\text{here "a=a_1=25" and } d = 6$

$\Rightarrow {a}_{n} = 25 + 6 \left(n - 1\right)$

$\textcolor{w h i t e}{\Rightarrow {a}_{n}} = 25 + 6 n - 6$

$\Rightarrow {a}_{n} = 6 n + 19$

$\Rightarrow {a}_{52} = \left(6 \times 52\right) + 19 = 331$