1. The problem is to find the missing numbers in the sequence: 4, __, 8, __, 16, __, 32, 64, __. 2. This sequence appears to be a geometric progression where each term is multiplied by 2 to get the next term. 3. The formula for the $n$th term of a geometric sequence is $$a_n = a_1 \times r^{n-1}$$ where $a_1$ is the first term and $r$ is the common ratio. 4. Here, $a_1 = 4$ and $r = 2$. 5. Calculate the missing terms: - The 2nd term: $$a_2 = 4 \times 2^{2-1} = 4 \times 2 = 8$$ but 8 is already the 3rd term, so the 2nd term must be halfway between 4 and 8, which is 6 (if the pattern is not strictly geometric, but let's check the pattern carefully). 6. Actually, the given sequence is 4, __, 8, __, 16, __, 32, 64, __. Let's check the pattern by positions: - 1st term: 4 - 3rd term: 8 - 5th term: 16 - 7th term: 32 - 8th term: 64 7. The terms at odd positions are doubling each time: 4, 8, 16, 32, 64. 8. The missing terms at even positions are unknown; since the odd terms double, the even terms might be the average of the adjacent odd terms. 9. Calculate the 2nd term as average of 4 and 8: $$\frac{4 + 8}{2} = 6$$ 10. Calculate the 4th term as average of 8 and 16: $$\frac{8 + 16}{2} = 12$$ 11. Calculate the 6th term as average of 16 and 32: $$\frac{16 + 32}{2} = 24$$ 12. Calculate the 9th term as average of 64 and next term (unknown), but since 64 is the last known term, we cannot find the 9th term. 13. So the missing terms are 6, 12, 24, and the last missing term is unknown. Final sequence: 4, 6, 8, 12, 16, 24, 32, 64, __