حل السؤال 20، 4MA1/2H نوفمبر 2021: مجموع المتتابعة الحسابية

1. 1First term = k
2. 2Second term = 3k/4
3. 3Common difference d = (3k/4) − k = −k/4
4. 415th term = k + 14d = k + 14(−k/4)
5. 5k + 14(−k/4) = k − (14k)/4 = k − 3.5k = −2.5k
6. 6But 15th term is given as 90 + 2k
7. 7So: −2.5k = 90 + 2k
8. 8−2.5k − 2k = 90
9. 9−4.5k = 90
10. 10k = 90 / (−4.5) = −20
11. 11Now first term a = k = −20
12. 12Common difference d = −k/4 = −(−20)/4 = 20/4 = 5
13. 13Sum of first 30 terms: S₃₀ = (30/2)[2a + (30-1)d]
14. 14S₃₀ = 15[2(−20) + 29×5]
15. 15S₃₀ = 15[-40 + 145]
16. 16S₃₀ = 15[105]
17. 17S₃₀ = 1575

Answer1575