Господин Экзамен
Решение для a13=-21,4 и a17=8,2 на арифметическую прогрессию
Решение
Вы ввели
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a13=-21,4 и a17=8,2
Найдено в тексте задачи:
Первый член: a1 = ?
n-член an (n = 16 + 1 = 17)
Разность: d = ?
Другие члены: a13 = -(107/5) a17 = (41/5)
Пример: ?
Найти члены от 1 до 17
Найти члены от 1 до 17
Решение
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a_n - a_k
d = ---------
n - k
$$d = \frac{- a_{k} + a_{n}}{- k + n}$$
a_1 = a_n + d*(-1 + n)
$$a_{1} = d \left(n - 1\right) + a_{n}$$
(-1 + n)*(a_n - a_k)
a_1 = a_n - --------------------
n - k
$$a_{1} = a_{n} - \frac{\left(- a_{k} + a_{n}\right) \left(n - 1\right)}{- k + n}$$
a_17 - a_13
d = -----------
4
$$d = \frac{- a_{13} + a_{17}}{4}$$
a_17 - a_13
a_1 = a_17 - -----------*15
4
$$a_{1} = a_{17} - \frac{- a_{13} + a_{17}}{4} \cdot 15$$
41/5 + 107/5
d = ------------
4
$$d = \frac{\frac{41}{5} + \frac{107}{5}}{4}$$
41 41/5 + 107/5
a_1 = -- - ------------*16
5 4
$$a_{1} = \left(-1\right) \frac{\frac{41}{5} + \frac{107}{5}}{4} \cdot 16 + \frac{41}{5}$$
d = 37/5
$$d = \frac{37}{5}$$
a_1 = -551/5
$$a_{1} = - \frac{551}{5}$$
a_1 = -551/5
Пример
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...
Расширенный пример:
-551/5; -514/5; -477/5; -88; -403/5; -366/5; -329/5; -292/5; -51; -218/5; -181/5; -144/5; -107/5; -14; -33/5; 4/5; 41/5...
a1 = -551/5
$$a_{1} = - \frac{551}{5}$$
a2 = -514/5
$$a_{2} = - \frac{514}{5}$$
a3 = -477/5
$$a_{3} = - \frac{477}{5}$$
a4 = -88
$$a_{4} = -88$$
a5 = -403/5
$$a_{5} = - \frac{403}{5}$$
a6 = -366/5
$$a_{6} = - \frac{366}{5}$$
a7 = -329/5
$$a_{7} = - \frac{329}{5}$$
a8 = -292/5
$$a_{8} = - \frac{292}{5}$$
a9 = -51
$$a_{9} = -51$$
a10 = -218/5
$$a_{10} = - \frac{218}{5}$$
a11 = -181/5
$$a_{11} = - \frac{181}{5}$$
a12 = -144/5
$$a_{12} = - \frac{144}{5}$$
a13 = -107/5
$$a_{13} = - \frac{107}{5}$$
a14 = -14
$$a_{14} = -14$$
a15 = -33/5
$$a_{15} = - \frac{33}{5}$$
a16 = 4/5
$$a_{16} = \frac{4}{5}$$
a17 = 41/5
$$a_{17} = \frac{41}{5}$$
...
...
Сумма
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n*(a_1 + a_n)
S = -------------
2
$$S = \frac{n \left(a_{1} + a_{n}\right)}{2}$$
Сумма семнадцати членов
17*(-551/5 + 41/5)
S17 = ------------------
2
$$S_{17} = \frac{17 \left(- \frac{551}{5} + \frac{41}{5}\right)}{2}$$
S17 = -867
$$S_{17} = -867$$
S17 = -867
n-член
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Семнадцатый член
a_n = a_1 + d*(-1 + n)
$$a_{n} = d \left(n - 1\right) + a_{1}$$
a_17 = 41/5
$$a_{17} = \frac{41}{5}$$
a_17 = 41/5