Answer :

Answer:

4096

Step-by-step explanation:

When given the placement and the term and know that this is a geometric sequence, the best formula to use is an = a1(r)^n-1, where n is the placement, an is the nth term, a1 is the first term.

So we know that if n = 10, an is 512, but don't know a1 nor r. Again, we also know that at n = 15, an = 16384. So if were to represent both of them in the formula

512 = a1(r)^10-1 = a1(r)^9

16384 = a1(r)^15-1 = a1(r)^14

Simple algebra can help you solve it. First lets find r

16834 / (r)^14 = a1

512 = (16384/r^14)(r^9)

512 = (16834/r^5)

r^5 = 16834/512

r^5 = 2

Now lets find a1

512 = a1(2)^9

512 = a1(512) a1 = 1

Now we know that the formula is an = 1(2)^n-1

So the thirteenth term would be n = 13, so 1(2)^13-1 = 1(2)^12 = 4096

Hope that answers your question.