حل السؤال 23، 4MA1/1H يونيو 2021: مجموع المتتابعة الحسابية

1. 1a + d = 8.5
2. 2a + 4d = 13
3. 3Subtracting: (a + 4d) − (a + d) = 13 − 8.5
4. 43d = 4.5
5. 5d = 1.5
6. 6Substitute d = 1.5 into a + d = 8.5
7. 7a + 1.5 = 8.5
8. 8a = 7
9. 9Sum of first N terms: S_N = N/2 [2a + (N − 1)d]
10. 10S_N = N/2 [2(7) + (N − 1)(1.5)] = 292
11. 11N/2 [14 + 1.5(N − 1)] = 292
12. 12N/2 [14 + 1.5N − 1.5] = 292
13. 13N/2 [12.5 + 1.5N] = 292
14. 14N(12.5 + 1.5N)/2 = 292
15. 15N(1.5N + 12.5) = 584
16. 161.5N² + 12.5N − 584 = 0
17. 17Multiply by 2: 3N² + 25N − 1168 = 0
18. 18Use quadratic formula: N = [-25 ± √(25² − 4×3×(−1168))]/(2×3)
19. 19N = [-25 ± √(625 + 14016)]/6
20. 20N = [-25 ± √14641]/6
21. 21√14641 = 121
22. 22N = (−25 + 121)/6 or N = (−25 − 121)/6
23. 23N = 96/6 = 16 or N = −146/6 (discard negative)
24. 24N = 16

Answer16