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
Hatua ya 1: Tambua neno la kwanza (a) na uwiano wa kawaida (r) wa GP. Kutoka kwa mfuatano 2, 4, 8, : Neno la kwanza, a = 2. Uwiano wa kawaida, r = (4)/(2) = 2. Hatua ya 2: Andika fomula ya jumla ya maneno n ya GP. Kwa kuwa r > 1, fomula ya jumla ya maneno n (S_n) ni: S_n = (a(r^n - 1))/(r - 1) Hatua ya 3: Badilisha thamani za a na r kwenye fomula. S_n = (2(2^n - 1))/(2 - 1) S_n = (2(2^n - 1))/(1) S_n = 2(2^n - 1) Hatua ya 4: Weka usawa kulingana na sharti kwamba jumla ni kubwa kuliko 1,500,000. 2(2^n - 1) > 1,500,000 Hatua ya 5: Tatua usawa kwa n. Gawanya pande zote mbili kwa 2: (2(2^n - 1))/(2) > (1,500,000)/(2) 2^n - 1 > 750,000 Ongeza 1 kwa pande zote mbili: 2^n > 750,000 + 1 2^n > 750,001 Ili kutatua kwa n, chukua logariti ya pande zote mbili (kwa mfano, logariti ya msingi 10 au asili): (2^n) > (750,001) n (2) > (750,001) n > ((750,001))/((2)) Tumia kikokotoo kupata thamani za logariti: (750,001) ≈ 5.87506 (2) ≈ 0.30103 n > (5.87506)/(0.30103) n > 19.516 Hatua ya 6: Tafuta nambari kamili ndogo zaidi ya maneno n inayokidhi usawa. Kwa kuwa n lazima iwe nambari kamili (idadi ya maneno), na n lazima iwe kubwa kuliko 19.516, nambari kamili ndogo zaidi inayokidhi sharti hili ni 20. Nambari ndogo zaidi ya maneno ambayo itatoa jumla kubwa kuliko 1,500,000 ni 20. 20 That's 2 down. 3 left today — send the next one.