Question

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`?

Answer 1

`a_(52)=-1008`

Explanation:

We can write the nth term of the sequence:

`a_n=a_1+d*(n-1)`

So, we have `a_n=12-20*(n-1)`.

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

`a_(52)=12-20*(52-1)=`
`= 12-20(51)=12-1020=-1008`