Question

Find the sixth term of the geometric sequence. 10, -5, 5/2

Answer 1

Hey there!

Arithmetic sequences are made up of terms that are added or subtracted, and geometric sequences are made up of terms that are multiplied or divided.

Given this info, we can see that we go from 10 to -5. Because we know that this is geometric, we see that we must divide by -2 in our sequence.

We can see that this is true because -5/-2=5/2.

Now, we could simply continue dividing by negative two to get our answer, which is -5/16.

You could easily do that with a calculator, but if you had to find a term that was farther from the first term, that would take forever to do with a calculator, so there is an equation that you can use and plug in your numbers to find the answer quickly.

$a_{n} = ar^{n-1}$, where $a_{n}$ is the number of term in the sequence (6 in this problem), a is the first term of the sequence (10), and r is the common ratio (-1/2).

I hope this helps!