1. The problem is to find the missing numbers in the sequence: 10 → 7 → [blank] → 1 → [blank] → -5. 2. First, observe the pattern in the given numbers: 10, 7, 1, -5. 3. Calculate the differences between the known consecutive terms: - From 10 to 7: $7 - 10 = -3$ - From 1 to -5: $-5 - 1 = -6$ 4. Notice the differences are decreasing by 3 each time: -3, then -6. 5. Let's check the difference between 7 and the first blank term, and between the first blank term and 1. 6. Assume the difference between 7 and the first blank is $d_1$, and between the first blank and 1 is $d_2$. 7. Since the differences seem to decrease by 3, and the first difference is -3, the next difference should be -4.5 (midway between -3 and -6) or follow a pattern of subtracting 3 each step. 8. Alternatively, check if the differences decrease by 3 each step: - First difference: $-3$ - Second difference: $-3 - 3 = -6$ But from 7 to blank and blank to 1, we have two differences, so the pattern might be: - 10 to 7: -3 - 7 to blank: -2 - blank to 1: -3 - 1 to blank: -6 This is inconsistent. 9. Another approach: check if the differences decrease by 3 each step: - 10 to 7: -3 - 7 to blank: -4.5 - blank to 1: -6 This fits a pattern of decreasing by 1.5 each time. 10. Calculate the first blank: $$\text{First blank} = 7 + (-4.5) = 2.5$$ 11. Calculate the second blank: $$\text{Second blank} = 1 + (-5.5) = -4.5$$ 12. But the second blank is between 1 and -5, so difference is $-5 - 1 = -6$, so the second blank should be: $$\text{Second blank} = 1 + (-3) = -2$$ 13. Re-examining, the differences between terms are: - 10 to 7: -3 - 7 to blank: -2 - blank to 1: -4 - 1 to blank: -6 This is inconsistent. 14. Let's try arithmetic progression with common difference $d$: $$a_1 = 10$$ $$a_2 = 7 = 10 + d$$ So, $d = -3$ Then: $$a_3 = 7 + d = 7 - 3 = 4$$ $$a_4 = 4 + d = 4 - 3 = 1$$ $$a_5 = 1 + d = 1 - 3 = -2$$ $$a_6 = -2 + d = -2 - 3 = -5$$ 15. The missing numbers are 4 and -2. Final answer: $$\boxed{4 \text{ and } -2}$$