This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Huu hapa ni ufumbuzi wa swali lako: Step 1: Tafuta tofauti kati ya namba zinazofuatana katika mfuatano. Mfuatano uliotolewa ni 1, 2, 6, 22, 45, \_, \_. Tafuta tofauti kati ya namba zinazofuatana: • Tofauti ya kwanza: 2 - 1 = 1 • Tofauti ya pili: 6 - 2 = 4 • Tofauti ya tatu: 22 - 6 = 16 • Tofauti ya nne: 45 - 22 = 23 Step 2: Tambua muundo wa tofauti. Tofauti zilizopatikana ni 1, 4, 16, 23. Tunaweza kuona muundo ufuatao: • 1 = (2-1)^2 = 1^2 • 4 = (3-1)^2 = 2^2 • 16 = (4-1)^2 + 7 = 3^2 + 7 = 9 + 7 • 23 = (5-1)^2 + 7 = 4^2 + 7 = 16 + 7 Muundo unaonekana kuwa: Kwa n=1, 2: Tofauti ya n-th ni (n)^2. (Hapa n inawakilisha nafasi ya tofauti, si nafasi ya namba kwenye mfuatano). Au, kwa kutumia nafasi ya namba kwenye mfuatano (k): a_k - a_k-1 = (k-1)^2 kwa k=2, 3. a_2 - a_1 = (2-1)^2 = 1^2 = 1. a_3 - a_2 = (3-1)^2 = 2^2 = 4. Na kwa k 4: a_k - a_k-1 = (k-1)^2 + 7. a_4 - a_3 = (4-1)^2 + 7 = 3^2 + 7 = 9 + 7 = 16. a_5 - a_4 = (5-1)^2 + 7 = 4^2 + 7 = 16 + 7 = 23. Step 3: Tafuta namba mbili zinazofuata katika mfuatano. Tutatumia muundo a_k = a_k-1 + (k-1)^2 + 7 kwa k 4. Namba ya sita (a_6): a_6 = a_5 + (6-1)^2 + 7 a_6 = 45 + 5^2 + 7 a_6 = 45 + 25 + 7 a_6 = 70 + 7 = 77. Namba ya saba (a_7): a_7 = a_6 + (7-1)^2 + 7 a_7 = 77 + 6^2 + 7 a_7 = 77 + 36 + 7 a_7 = 113 + 7 = 120. Step 4: Kokotoa jumla ya namba mbili zinazofuata. Namba mbili zinazofuata ni 77 na 120. Jumla yao ni 77 + 120 = 197. Jumla ya namba mbili zinazofuata ni 197. 3 done, 2 left today. You're making progress.