5. Последовательность составлена следующим образом: если а – некоторый член последовательности, b – следующий за ним член, то b = –3а. Зная первый член последовательности, продолжите запись, заканчивая шестым членом:

json { "question": "5. \\(\u\)041f\\(\u\)043e\\(\u\)0441\\(\u\)043b\\(\u\)0435\\(\u\)0434\\(\u\)043e\\(\u\)0432\\(\u\)0430\\(\u\)0442\\(\u\)0435\\(\u\)043b\\(\u\)044c\\(\u\)043d\\(\u\)043e\\(\u\)0441\\(\u\)0442\\(\u\)044c\\(\u\)0442\\(\u\)044c\\(\u\)0441\\(\u\)043e\\(\u\)0441\\(\u\)0442\\(\u\)0430\\(\u\)0432\\(\u\)043b\\(\u\)0435\\(\u\)043d\\(\u\)0430\\(\u\)00a0\\(\u\)0441\\(\u\)043b\\(\u\)0435\\(\u\)0434\\(\u\)0443\\(\u\)044e\\(\u\)0449\\(\u\)0438\\(\u\)043c\\(\u\)00a0\\(\u\)043e\\(\u\)0431\\(\u\)0440\\(\u\)0430\\(\u\)0437\\(\u\)043e\\(\u\)043c:\\(\u\)00a0\\(\u\)0435\\(\u\)0441\\(\u\)043b\\(\u\)0438\\(\u\)00a0\\(\u\)0430\\(\u\)00a0–\\(\u\)00a0\\(\u\)043d\\(\u\)0435\\(\u\)043a\\(\u\)043e\\(\u\)0442\\(\u\)043e\\(\u\)0440\\(\u\)044b\\(\u\)0439\\(\u\)00a0\\(\u\)0447\\(\u\)043b\\(\u\)0435\\(\u\)043d\\(\u\)00a0\\(\u\)043f\\(\u\)043e\\(\u\)0441\\(\u\)043b\\(\u\)0435\\(\u\)0434\\(\u\)043e\\(\u\)0432\\(\u\)0430\\(\u\)0442\\(\u\)0435\\(\u\)043b\\(\u\)044c\\(\u\)043d\\(\u\)043e\\(\u\)0441\\(\u\)0442\\(\u\)0438,\\(\u\)00a0\\(\u\)0432\\(\u\)00a0–\\(\u\)00a0\\(\u\)0441\\(\u\)043b\\(\u\)0435\\(\u\)0434\\(\u\)0443\\(\u\)044e\\(\u\)0449\\(\u\)0438\\(\u\)0439\\(\u\)00a0\\(\u\)0437\\(\u\)0430\\(\u\)00a0\\(\u\)043d\\(\u\)0438\\(\u\)043c\\(\u\)00a0\\(\u\)0447\\(\u\)043b\\(\u\)0435\\(\u\)043d,\\(\u\)00a0\\(\u\)0442\\(\u\)043e\\(\u\)00a0\\(\u\)0432\\(\u\)00a0=\\(\u\)00a0-3а.\\(\u\)00a0\\(\u\)0417\\(\u\)043d\\(\u\)0430\\(\u\)044f\\(\u\)00a0\\(\u\)043f\\(\u\)0435\\(\u\)0440\\(\u\)0432\\(\u\)044b\\(\u\)0439\\(\u\)00a0\\(\u\)0447\\(\u\)043b\\(\u\)0435\\(\u\)043d\\(\u\)00a0\\(\u\)043f\\(\u\)043e\\(\u\)0441\\(\u\)043b\\(\u\)0435\\(\u\)0434\\(\u\)043e\\(\u\)0432\\(\u\)0430\\(\u\)0442\\(\u\)0435\\(\u\)043b\\(\u\)044c\\(\u\)043d\\(\u\)043e\\(\u\)0441\\(\u\)0442\\(\u\)0438,\\(\u\)00a0\\(\u\)043f\\(\u\)0440\\(\u\)043e\\(\u\)0434\\(\u\)043e\\(\u\)043b\\(\u\)0436\\(\u\)0438\\(\u\)0442\\(\u\)0435\\(\u\)00a0\\(\u\)0437\\(\u\)0430\\(\u\)043f\\(\u\)0438\\(\u\)0441\\(\u\)044c,\\(\u\)00a0\\(\u\)0437\\(\u\)0430\\(\u\)043a\\(\u\)0430\\(\u\)043d\\(\u\)0447\\(\u\)0438\\(\u\)0432\\(\u\)0430\\(\u\)044f\\(\u\)00a0\\(\u\)0448\\(\u\)0435\\(\u\)0441\\(\u\)0442\\(\u\)044b\\(\u\)043c\\(\u\)00a0\\(\u\)0447\\(\u\)043b\\(\u\)0435\\(\u\)043d\\(\u\)043e\\(\u\)043c:", "answer": "

Привет! Давай разберём эту задачку про последовательность.

У нас есть правило: каждый следующий член последовательности в 3 раза меньше предыдущего (или, если точнее, равен предыдущему, умноженному на -3).

Пусть первый член последовательности равен \(a_1\).

Тогда:

\(a_2 = -3 · a_1\)

\(a_3 = -3 · a_2 = -3 · (-3 · a_1) = (-3)^2 · a_1 = 9 · a_1\)

\(a_4 = -3 · a_3 = -3 · (9 · a_1) = -27 · a_1\)

\(a_5 = -3 · a_4 = -3 · (-27 · a_1) = 81 · a_1\)

\(a_6 = -3 · a_5 = -3 · (81 · a_1) = -243 · a_1\)

Итоговая запись:

\(a_1, -3a_1, 9a_1, -27a_1, 81a_1, -243a_1\)