# 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=12, d=-20?

Dec 7, 2017

${a}_{52} = - 1008$

#### Explanation:

We can write the nth term of the sequence:

${a}_{n} = {a}_{1} + d \cdot \left(n - 1\right)$

So, we have ${a}_{n} = 12 - 20 \cdot \left(n - 1\right)$.

To find the 52nd term we now substitute 52 for n:

${a}_{52} = 12 - 20 \cdot \left(52 - 1\right) =$
$= 12 - 20 \left(51\right) = 12 - 1020 = - 1008$