How do you find the formula for #a_n# for the arithmetic sequence #a_1=-4, a_5=16#?
Set up and solve a system of equations using the definition of the arithmetic sequence. Answer:
We know that from the general formula for arithmetic sequences:
So, we write out what we know:
Using the general formula for arithmetic sequences, the second equation becomes:
Now, we simply solve for d:
Therefore, the formula for the given arithmetic sequence is: