Question

50 ів, тільки зробіть завдання на тему: арифметична прогресія. зробити номер 727:

Answer 1

$a_{1} = 1.5 \: \: d = x \: \: a_{n} = 54 \: \: s_{n} = 999 \\ s_{n} = \frac{a_{1} + a_{n}}{2} \times n = 999 \\ \frac{1.5 + 54}{2} \times n = 999 \\ 27.75n = 999 \\ n = 36 \\ \\ a_{36} = a_{1} + 35d = 54 \\ 1.5 + 35d = 54 \\ 35d = 52.5 \\ d = 1.5$

$a_{1} = 0.2 \: \: d = x \: \: a_{n} = 5.2 \: \: s_{n} = 137.7 \\ s_{n} = \frac{a_{1} + a_{n}}{2} \times n =137.7 \\ \frac{0.2 + 5.2}{2} \times n = 137.7 \\ 2.7n = 137.7 \\ n = 51 \\ \\ a_{51} = a_{1} + 50d = 5.2 \\ 0.2 + 50d = 5.2 \\ 50d = 5 \\ d = 0.1$

$a_{1} = - 28 \: \: d = x \: \: n = 9 \: \: a_{n} = y \: \: s_{9} = 0 \\ s_{9} = \frac{a_{1} + a_{9} }{2} \times 9 = 0 \\ \frac{ - 28 + a_{9}}{2} \times 9 = 0 \\ (- 28 + a_{9}) \times 18 = 0 \\ a_{9} = 28 \\ a_{9} = a_{1} + 8d = 28 \\ - 28 + 8d = 28 \\ 8d = 56 \\ d = 7$

$a_{1} = 0.7 \: \: d = x \: \: n = 30 \: \: a_{n} = y \: \: s_{30} = 108 \\ s _{30} = \frac{a_{1} + a_{30}}{2} \times 30 = 108 \\ \frac{0.7 + a_{30} }{2} \times 30 = 108 \\ (0.7 + a_{30}) \times 60 = 216 \\ 0.7 + a_{30} = 3.6 \\a_{30} = 2.9 \\ \\ a_{30} =a_{1} + 29d = 2.9 \\ 0.7 + 29d = 2.9 \\ 29d = 2.2 \\ d = 0.07586$

$a_{1} = x \: \: d = y \: \: n = 14 \: \: a_{14} = 140 \: \: s_{14} = 1050 \\ s_{14} = \frac{a_{1} + a_{14}}{2} \times 14 = 1050 \\ \frac{a_{1} + 140}{2} \times 14 = 1050 \\ (a_{1} + 140) \times 28 = 2100 \\ a_{1} + 140 = 75 \\ a_{1} = - 65 \\ \\ a_{14} = a_{1} + 13d = 140 \\ - 65 + 13d = 140 \\ 13d = 205 \\ d = 15.8$

$a_{1} = x \: \: d = y \: \: n = 10 \: \: a_{10} = - 37 \: \: s_{10} = - 55 \\ s_{10} = \frac{a_{1} + a_{10}}{2} \times 10 = - 55 \\ (a_{1} - 37) \times 20 = - 110 \\ a_{1} - 37 = - 5.5 \\ a_{1} = 31.5 \\ \\ a_{10} = a_{1} + 9d = - 37 \\ 31.5 + 9d = - 37 \\ 9d = - 68.5 \\ d = 7.6$

$a_{1} = x \: \: d = 3 \: \: n = 31 \: \: a_{31} = y \: \: s_{31} = 0 \\ s_{31} = \frac{2a_{1} + 30d}{2} \times 31 = 0 \\ (a_{1} + 45) \times 31 = 0 \\ a_{1} = - 45 \\ \\ a_{31} = a_{1} + 30d = - 45 + 90 = 45$

$a_{1} = x \: \: d = \frac{1}{3} \: \: n = 37 \: \: a_{37} = y \: \: s_{37} = 209 \frac{2}{3} \\ s_{37} = \frac{2a_{1} + 36d}{2} \times 37 = 209 \frac{2}{3} \\ (a_{1} + 18d) \times 37 = 209 \frac{2}{3} = \frac{629}{3} \\ a_{1} + 6 = \frac{17}{3} \\ a_{1} = - \frac{1}{3} \\ \\ a_{37} = a_{1} + 36d = - \frac{1}{3} + 12 = \frac{35}{3} = 11 \frac{2}{3}$

сколько смогла