# If the first term in a geometric sequence is 7, and the third term is 63, what is the ninth term?

##### 1 Answer

Nov 8, 2015

567

#### Explanation:

We now that for the first term, a1, n=1 and a1 = 7. So we can begin with an equation like:

a*n = 7*n and this would give us

a1 = 7 which is good.

Now, we look at the a3 term when n=3. If we put this into our equation we get 21 which is NOT the right answer. But we know that 7*9 will give us 63. And we know that 3*3 will give us 9. So:

a3= 7(3*3) = 63 which is right.

Now we have a new equation:

a*n= 7(n^2)

And we need to see if this still works for a1 when n=1, which it does.

So we solve for the ninth term when n=9 and get:

a9: 7(9^2) = 567