Question

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

Answer 1

567

Explanation:

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

an = 7n 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 79 will give us 63. And we know that 33 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