Задача a5 =7,12 , a6=15,58 (на арифметическую прогрессию)

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_6 - a_5
d = ---------
        1    

$$d = \frac{- a_{5} + a_{6}}{1}$$

            a_6 - a_5  
a_1 = a_6 - ---------*4
                1      

$$a_{1} = a_{6} - 4 \frac{- a_{5} + a_{6}}{1}$$

    779   178
    --- - ---
     50    25
d = ---------
        1    

$$d = \frac{- \frac{178}{25} + \frac{779}{50}}{1}$$

            779   178  
            --- - ---  
      779    50    25  
a_1 = --- - ---------*5
       50       1      

$$a_{1} = - 5 \frac{- \frac{178}{25} + \frac{779}{50}}{1} + \frac{779}{50}$$

    423
d = ---
     50

$$d = \frac{423}{50}$$

      -668 
a_1 = -----
        25 

$$a_{1} = - \frac{668}{25}$$

Первый член

      -668 
a_1 = -----
        25 

$$a_{1} = - \frac{668}{25}$$

Разность

    423
d = ---
     50

$$d = \frac{423}{50}$$

Пример

...

Расширенный пример:

-668/25; -913/50; -49/5; -67/50; 178/25; 779/50...

     -668 
a1 = -----
       25 

$$a_{1} = - \frac{668}{25}$$

     -913 
a2 = -----
       50 

$$a_{2} = - \frac{913}{50}$$

a3 = -49/5

$$a_{3} = - \frac{49}{5}$$

     -67 
a4 = ----
      50 

$$a_{4} = - \frac{67}{50}$$

     178
a5 = ---
      25

$$a_{5} = \frac{178}{25}$$

     779
a6 = ---
      50

$$a_{6} = \frac{779}{50}$$

...

n-член

Шестой член

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

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

      779
a_6 = ---
       50

$$a_{6} = \frac{779}{50}$$

Сумма

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

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

Сумма шести членов

     -1671 
S6 = ------
       50  

$$S_{6} = - \frac{1671}{50}$$