for follow a specific format.
an=a1+(n−1)d
In this form,
a1 is the first term in a given sequence,
d is the common difference from one term to the next, and
an is the
nth term in the sequence. For this exercise, the first term is
a1=-6. Let's observe the other terms to determine the common difference
d.
-6→-3-9→-3-12→-3-15…
As we can see
d=-3. By substituting these two values we found into the explicit equation and simplifying, we can find the formula for this sequence.
an=a1+(n−1)d
an=-6+(n−1)(-3)
an=-6−3n+3
an=-3n−3
This equation can be used to find any term in the given sequence. To find
a10, the
10th term in the sequence, we substitute
10 for
n.
an=-3n−3
a10=-3(10)−3
a10=-30−3
a10=-33
The
10th term in the sequence is
-33.