Subjects algebra

Sequence Gaps Cdea52

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1. **State the problem:** We have the sequence 11 → 8 → ? → 2 → ? → -4 and need to find the missing terms. 2. **Identify the pattern:** Look at the differences between known terms. 3. Calculate the difference from 11 to 8: $$8 - 11 = -3$$ 4. Calculate the difference from 2 to -4: $$-4 - 2 = -6$$ 5. Notice the differences might be decreasing by 1.5 each step: from -3 to -4.5 to -6. 6. Find the missing term after 8 by subtracting 4.5: $$8 - 4.5 = 3.5$$ 7. Find the missing term after 2 by subtracting 5.25 (halfway between 4.5 and 6 is 5.25): $$2 - 5.25 = -3.25$$ 8. Verify the sequence: $$11, 8, 3.5, 2, -3.25, -4$$ 9. The differences are: $$-3, -4.5, -1.5, -5.25, -0.75$$ which do not form a simple arithmetic progression, so check for another pattern. 10. Alternatively, check if the differences decrease by 1.5 each step: $$11 \to 8: -3$$ $$8 \to 5: -3$$ (try 5 as missing term) $$5 \to 2: -3$$ $$2 \to -1: -3$$ (try -1 as missing term) $$-1 \to -4: -3$$ 11. This suggests the missing terms are 5 and -1. **Final answer:** The missing terms are 5 and -1. Sequence: 11 → 8 → 5 → 2 → -1 → -4