# 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=-19, d=-3?

May 29, 2017

${a}_{52} = - 172 , {a}_{n} = - 3 n - 16$

#### Explanation:

$\text{in an arithmetic sequence we can find any term using}$

• a_n= a_1+(n-1)dlarr" nth term formula"

$\Rightarrow {a}_{52} = - 19 + \left(51 \times - 3\right) = - 172$

$\textcolor{b l u e}{\text{ the explicit formula }}$

$\text{found using the nth term formula}$

$\text{with " a_1=-19" and } d = - 3$

$\Rightarrow {a}_{n} = - 19 - 3 \left(n - 1\right)$

$\textcolor{w h i t e}{\times \times} = - 19 - 3 n + 3$

$\textcolor{w h i t e}{\times \times} = - 3 n - 16 \leftarrow \textcolor{red}{\text{ explicit formula}}$

$\textcolor{b l u e}{\text{As a check}}$

${a}_{52} = \left(- 3 \times 52\right) - 16 = - 172 \rightarrow \text{ True}$