Question

Find the 39th term.
-15, -10, -5, 0, 5, ...
39th term = [?]

Answer 1

The explicit arithmetic formula can be used to find the 39th term of this sequence.

`a_(n) = a_(1) + d(n-1)`

In order to use this formula, we must know a_1, the first term, and , the common difference.

In this case, the first term is given as -15.

The difference can be found by looking at the difference between each following term. In this case, d = +5.

(Notice to get from -15 to -10, we add 5, to get from -10 to -5, we add 5, etc.)

Now that we have everything we need, we can plug everything in to find the 39th term:

`a_(39) = -15 + 5(39-1)\\a_(39) = -15 + 190\\a_(39) = 175`

The 39th term of this sequence is 175.

*Note n represents the term number we are trying to find. That's why we substituted 39 for n when plugging everything into the formula.
`a_(39)` denotes the 39th term