Задача Найди сумму первых 18 чл ... ли a10= -5,3 a22=17,5 (на арифметическую прогрессию)

Вы ввели

Найди сумму первых 18 членов арифметической прогрессии, если a10= -5,3 
a22=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

    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

$$a_{1} = - \frac{112}{5}$$

Первый член

a_1 = -112/5

$$a_{1} = - \frac{112}{5}$$

Разность

    19
d = --
    10

$$d = \frac{19}{10}$$

Сумма

    n*(a_1 + a_n)
S = -------------
          2      

$$S = \frac{n \left(a_{1} + a_{n}\right)}{2}$$

      -539 
S22 = -----
        10 

$$S_{22} = - \frac{539}{10}$$

Пример

...

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

$$a_{22} = \frac{35}{2}$$

...

n-член

a_n = a_1 + d*(-1 + n)

$$a_{n} = a_{1} + d \left(n - 1\right)$$

a_22 = 35/2

$$a_{22} = \frac{35}{2}$$