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.
