This English question involves literary analysis, grammar, or writing skills. The detailed response below provides a well-structured answer with supporting evidence and clear explanations.
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Hapa kuna suluhisho la swali la 1(a): 1. (a) Mfuatano wa hesabu umetungwa na nambari zinazogawanyika hasa kwa 4, huku nambari ya mwisho ikiwa 928. Nambari ya kwanza ni 4. Step 1: Determine the common difference. Kwa kuwa nambari zote katika mfuatano zinagawanyika hasa kwa 4, tofauti ya kawaida kati ya nambari mfululizo lazima iwe 4. d = 4 Tofauti ya kawaida ni 4. Step 2: Determine the number of terms in the series. Tunatumia formula ya nambari ya n-th katika mfuatano wa hesabu: L = a + (n-1)d. Tuna L = 928, a = 4, na d = 4. 928 &= 4 + (n-1)4 \\ 928 - 4 &= (n-1)4 \\ 924 &= 4(n-1) \\ (924)/(4) &= n-1 \\ 231 &= n-1 \\ n &= 231 + 1 \\ n &= 232 Idadi ya nambari katika mfuatano ni 232. Step 3: Determine the sum of all terms. Tunatumia formula ya jumla ya mfuatano wa hesabu: S_n = (n)/(2)(a + L). Tuna n = 232, a = 4, na L = 928. S_232 &= (232)/(2)(4 + 928) \\ S_232 &= 116(932) \\ S_232 &= 108112 Jumla ya nambari zote ni 108,112. Step 4: Determine the 80th term. Tunatumia formula ya nambari ya n-th: a_n = a + (n-1)d. Tunataka kupata nambari ya 80, kwa hivyo n = 80. Tuna a = 4 na d = 4. a_80 &= 4 + (80-1)4 \\ a_80 &= 4 + (79)4 \\ a_80 &= 4 + 316 \\ a_80 &= 320 Nambari ya 80 ni 320. Tuma swali linalofuata 📸