Прогрессии/ Арифметическая прогрессия/ а10=-5,3 а22=17,5

Задача а10=-5,3 а22=17,5 (на арифметическую прогрессию)

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Решение

Вы ввели [src]
а10=-5,3
а22=17,5
Найдено в тексте задачи:
Первый член: a1 = ?
n-член an (n = 21 + 1 = 22)
Разность: d = ?
Другие члены: a10 = -(53/10)
a22 = (35/2)
Пример: ?
Найти члены от 1 до 22
Решение [src]
    a_n - a_k
d = ---------
      n - k
$$d = \frac{- a_{k} + a_{n}}{- k + n}$$
a_1 = a_n + d*(-1 + n)
$$a_{1} = a_{n} + d \left(n - 1\right)$$
            (-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_22 - a_10
d = -----------
         12
$$d = \frac{- a_{10} + a_{22}}{12}$$
             a_22 - a_10   
a_1 = a_22 - -----------*20
                  12
$$a_{1} = a_{22} - 20 \frac{- a_{10} + a_{22}}{12}$$
           53
    35/2 + --
           10
d = ---------
        12
$$d = \frac{\frac{53}{10} + \frac{35}{2}}{12}$$
                  53   
           35/2 + --   
      35          10   
a_1 = -- - ---------*21
      2        12
$$a_{1} = - 21 \frac{\frac{53}{10} + \frac{35}{2}}{12} + \frac{35}{2}$$
    19
d = --
    10
$$d = \frac{19}{10}$$
a_1 = -112/5
$$a_{1} = - \frac{112}{5}$$
Пример [src]
...
Расширенный пример:
-112/5; -41/2; -93/5; -167/10; -74/5; -129/10; -11; -91/10; -36/5; -53/10; -17/5; -3/2; 2/5; 23/10; 21/5; 61/10; 8; 99/10; 59/5; 137/10; 78/5; 35/2...
a1 = -112/5
$$a_{1} = - \frac{112}{5}$$
a2 = -41/2
$$a_{2} = - \frac{41}{2}$$
a3 = -93/5
$$a_{3} = - \frac{93}{5}$$
     -167 
a4 = -----
       10
$$a_{4} = - \frac{167}{10}$$
a5 = -74/5
$$a_{5} = - \frac{74}{5}$$
     -129 
a6 = -----
       10
$$a_{6} = - \frac{129}{10}$$
a7 = -11
$$a_{7} = -11$$
     -91 
a8 = ----
      10
$$a_{8} = - \frac{91}{10}$$
a9 = -36/5
$$a_{9} = - \frac{36}{5}$$
      -53 
a10 = ----
       10
$$a_{10} = - \frac{53}{10}$$
a11 = -17/5
$$a_{11} = - \frac{17}{5}$$
a12 = -3/2
$$a_{12} = - \frac{3}{2}$$
a13 = 2/5
$$a_{13} = \frac{2}{5}$$
      23
a14 = --
      10
$$a_{14} = \frac{23}{10}$$
a15 = 21/5
$$a_{15} = \frac{21}{5}$$
      61
a16 = --
      10
$$a_{16} = \frac{61}{10}$$
a17 = 8
$$a_{17} = 8$$
      99
a18 = --
      10
$$a_{18} = \frac{99}{10}$$
a19 = 59/5
$$a_{19} = \frac{59}{5}$$
      137
a20 = ---
       10
$$a_{20} = \frac{137}{10}$$
a21 = 78/5
$$a_{21} = \frac{78}{5}$$
a22 = 35/2
$$a_{22} = \frac{35}{2}$$
...
Разность [src]
    19
d = --
    10
$$d = \frac{19}{10}$$
Первый член [src]
a_1 = -112/5
$$a_{1} = - \frac{112}{5}$$
Сумма [src]
    n*(a_1 + a_n)
S = -------------
          2
$$S = \frac{n \left(a_{1} + a_{n}\right)}{2}$$
      -539 
S22 = -----
        10
$$S_{22} = - \frac{539}{10}$$
n-член [src]
a_n = a_1 + d*(-1 + n)
$$a_{n} = a_{1} + d \left(n - 1\right)$$
a_22 = 35/2
$$a_{22} = \frac{35}{2}$$