Question

An arithmetic sequence has this recursive formula:

a₁ = 5
an = an-1-4
What is the explicit formula for this sequence?

Answer 1

`a_n = 5 + (n-1)(-4)`

Explanation:

So the explicit formula is generally defined as
`a_n = a_1 + d(n-1)`. where d is essentially the "slope", basically how much it's changing from term to term. anyways if you look at the recursive formula you'll notice it's taking the previous term and subtracting 4. This is what d is going to be, -4 and since a_1 is given you plug that in as well. This gives you the equation

`a_n = 5 -4(n-1)` which can also be written as
`a_n = 5 + (n-1)(-4)`