Subjects algebra

Sheep Height Sequence

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1. Problem: You saw a group of sheep with a total of 28 legs and 14 eyes. How many sheep are there? - Each sheep has 4 legs and 2 eyes. - Let the number of sheep be $x$. - Total legs: $4x = 28$. - Total eyes: $2x = 14$. 2. Solve for $x$ using legs: $$4x = 28$$ $$x = \frac{28}{4} = 7$$ 3. Check with eyes: $$2x = 14$$ $$x = \frac{14}{2} = 7$$ 4. Both match, so the number of sheep is $7$. --- 5. Problem: Given the height relations: - Abdullah is taller than Mohammad. - Mohammad is shorter than Khalid and taller than Mahmoud. Who is the shortest? 6. From the relations: - $A > M$ - $K > M > Ma$ 7. Ordering from tallest to shortest: $$K > A > M > Ma$$ 8. The shortest is Mahmoud. --- 9. Problem: Find the 999th term of the sequence $55, 60, 65, \ldots$ 10. This is an arithmetic sequence with first term $a_1 = 55$ and common difference $d = 5$. 11. The $n$th term formula: $$a_n = a_1 + (n-1)d$$ 12. Substitute $n=999$: $$a_{999} = 55 + (999-1) \times 5 = 55 + 998 \times 5 = 55 + 4990 = 5045$$ 13. The 999th term is $5045$. Final answers: - Number of sheep: 7 - Shortest person: Mahmoud - 999th term: 5045