Задача найди разность арифметиче ... ов прогрессии равна 418,8 (на арифметическую прогрессию)

Вы ввели

найди разность арифметической прогрессии, если а1=0,91, а сумма первых тридцати членов  прогрессии равна 418,8

Найдено в тексте задачи:

Первый член: a1 = (91/100)

n-член an (n = 29 + 1 = 30)

Разность: d = 2*(((2094/5))/30-((91/100)))/(30-1)

Другие члены: a1 = (91/100)

Пример: ?

Найти члены от 1 до 30

n-член

Тридцатый член

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

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

       2701
a_30 = ----
       100 

$$a_{30} = \frac{2701}{100}$$

Разность

$d = 2*(S_k / k - a_1) / (k - 1)

$d = 2*(S_30 / 30 - a_1) / (30 - 1)$

$d = 2*(S_30 / 30 - a_1) / 30$

подставляем

$d = 2*((418,8)/30 - (0,91)) / (30 - 1)$

d = 9/10

$$d = \frac{9}{10}$$

Пример

...

Расширенный пример:

91/100; 181/100; 271/100; 361/100; 451/100; 541/100; 631/100; 721/100; 811/100; 901/100; 991/100; 1081/100; 1171/100; 1261/100; 1351/100; 1441/100; 1531/100; 1621/100; 1711/100; 1801/100; 1891/100; 1981/100; 2071/100; 2161/100; 2251/100; 2341/100; 2431/100; 2521/100; 2611/100; 2701/100...

      91
a1 = ---
     100

$$a_{1} = \frac{91}{100}$$

     181
a2 = ---
     100

$$a_{2} = \frac{181}{100}$$

     271
a3 = ---
     100

$$a_{3} = \frac{271}{100}$$

     361
a4 = ---
     100

$$a_{4} = \frac{361}{100}$$

     451
a5 = ---
     100

$$a_{5} = \frac{451}{100}$$

     541
a6 = ---
     100

$$a_{6} = \frac{541}{100}$$

     631
a7 = ---
     100

$$a_{7} = \frac{631}{100}$$

     721
a8 = ---
     100

$$a_{8} = \frac{721}{100}$$

     811
a9 = ---
     100

$$a_{9} = \frac{811}{100}$$

      901
a10 = ---
      100

$$a_{10} = \frac{901}{100}$$

      991
a11 = ---
      100

$$a_{11} = \frac{991}{100}$$

      1081
a12 = ----
      100 

$$a_{12} = \frac{1081}{100}$$

      1171
a13 = ----
      100 

$$a_{13} = \frac{1171}{100}$$

      1261
a14 = ----
      100 

$$a_{14} = \frac{1261}{100}$$

      1351
a15 = ----
      100 

$$a_{15} = \frac{1351}{100}$$

      1441
a16 = ----
      100 

$$a_{16} = \frac{1441}{100}$$

      1531
a17 = ----
      100 

$$a_{17} = \frac{1531}{100}$$

      1621
a18 = ----
      100 

$$a_{18} = \frac{1621}{100}$$

      1711
a19 = ----
      100 

$$a_{19} = \frac{1711}{100}$$

      1801
a20 = ----
      100 

$$a_{20} = \frac{1801}{100}$$

      1891
a21 = ----
      100 

$$a_{21} = \frac{1891}{100}$$

      1981
a22 = ----
      100 

$$a_{22} = \frac{1981}{100}$$

      2071
a23 = ----
      100 

$$a_{23} = \frac{2071}{100}$$

      2161
a24 = ----
      100 

$$a_{24} = \frac{2161}{100}$$

      2251
a25 = ----
      100 

$$a_{25} = \frac{2251}{100}$$

      2341
a26 = ----
      100 

$$a_{26} = \frac{2341}{100}$$

      2431
a27 = ----
      100 

$$a_{27} = \frac{2431}{100}$$

      2521
a28 = ----
      100 

$$a_{28} = \frac{2521}{100}$$

      2611
a29 = ----
      100 

$$a_{29} = \frac{2611}{100}$$

      2701
a30 = ----
      100 

$$a_{30} = \frac{2701}{100}$$

...

Первый член

       91
a_1 = ---
      100

$$a_{1} = \frac{91}{100}$$

Сумма

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

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

Сумма тридцати членов

         / 91   2701\
      30*|--- + ----|
         \100   100 /
S30 = ---------------
             2       

$$S_{30} = \frac{30 \cdot \left(\frac{91}{100} + \frac{2701}{100}\right)}{2}$$

S30 = 2094/5

$$S_{30} = \frac{2094}{5}$$