Задача В арифметической прогресс ... разность этой прогрессии. (на арифметическую прогрессию)

Вы ввели

в арифметической прогрессии первый член а1 = 7,5, s55 = 1650. определи
разность этой прогрессии.

Найдено в тексте задачи:

Первый член: a1 = (15/2)

n-член an (n = 54 + 1 = 55)

Разность: d = 2*((1650)/55-((15/2)))/(55-1)

Другие члены: a1 = (15/2)

Пример: ?

Найти члены от 1 до 55

Сумма

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

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

      55*(15/2 + 105/2)
S55 = -----------------
              2        

$$S_{55} = \frac{55 \cdot \left(\frac{15}{2} + \frac{105}{2}\right)}{2}$$

S55 = 1650

$$S_{55} = 1650$$

Разность

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

$d = 2*(S_55 / 55 - a_1) / (55 - 1)$

$d = 2*(S_55 / 55 - a_1) / 55$

подставляем

$d = 2*((1650)/55 - (7,5)) / (55 - 1)$

d = 5/6

$$d = \frac{5}{6}$$

Пример

...

Расширенный пример:

15/2; 25/3; 55/6; 10; 65/6; 35/3; 25/2; 40/3; 85/6; 15; 95/6; 50/3; 35/2; 55/3; 115/6; 20; 125/6; 65/3; 45/2; 70/3; 145/6; 25; 155/6; 80/3; 55/2; 85/3; 175/6; 30; 185/6; 95/3; 65/2; 100/3; 205/6; 35; 215/6; 110/3; 75/2; 115/3; 235/6; 40; 245/6; 125/3; 85/2; 130/3; 265/6; 45; 275/6; 140/3; 95/2; 145/3; 295/6; 50; 305/6; 155/3; 105/2...

a1 = 15/2

$$a_{1} = \frac{15}{2}$$

a2 = 25/3

$$a_{2} = \frac{25}{3}$$

a3 = 55/6

$$a_{3} = \frac{55}{6}$$

a4 = 10

$$a_{4} = 10$$

a5 = 65/6

$$a_{5} = \frac{65}{6}$$

a6 = 35/3

$$a_{6} = \frac{35}{3}$$

a7 = 25/2

$$a_{7} = \frac{25}{2}$$

a8 = 40/3

$$a_{8} = \frac{40}{3}$$

a9 = 85/6

$$a_{9} = \frac{85}{6}$$

a10 = 15

$$a_{10} = 15$$

a11 = 95/6

$$a_{11} = \frac{95}{6}$$

a12 = 50/3

$$a_{12} = \frac{50}{3}$$

a13 = 35/2

$$a_{13} = \frac{35}{2}$$

a14 = 55/3

$$a_{14} = \frac{55}{3}$$

a15 = 115/6

$$a_{15} = \frac{115}{6}$$

a16 = 20

$$a_{16} = 20$$

a17 = 125/6

$$a_{17} = \frac{125}{6}$$

a18 = 65/3

$$a_{18} = \frac{65}{3}$$

a19 = 45/2

$$a_{19} = \frac{45}{2}$$

a20 = 70/3

$$a_{20} = \frac{70}{3}$$

a21 = 145/6

$$a_{21} = \frac{145}{6}$$

a22 = 25

$$a_{22} = 25$$

a23 = 155/6

$$a_{23} = \frac{155}{6}$$

a24 = 80/3

$$a_{24} = \frac{80}{3}$$

a25 = 55/2

$$a_{25} = \frac{55}{2}$$

a26 = 85/3

$$a_{26} = \frac{85}{3}$$

a27 = 175/6

$$a_{27} = \frac{175}{6}$$

a28 = 30

$$a_{28} = 30$$

a29 = 185/6

$$a_{29} = \frac{185}{6}$$

a30 = 95/3

$$a_{30} = \frac{95}{3}$$

a31 = 65/2

$$a_{31} = \frac{65}{2}$$

a32 = 100/3

$$a_{32} = \frac{100}{3}$$

a33 = 205/6

$$a_{33} = \frac{205}{6}$$

a34 = 35

$$a_{34} = 35$$

a35 = 215/6

$$a_{35} = \frac{215}{6}$$

a36 = 110/3

$$a_{36} = \frac{110}{3}$$

a37 = 75/2

$$a_{37} = \frac{75}{2}$$

a38 = 115/3

$$a_{38} = \frac{115}{3}$$

a39 = 235/6

$$a_{39} = \frac{235}{6}$$

a40 = 40

$$a_{40} = 40$$

a41 = 245/6

$$a_{41} = \frac{245}{6}$$

a42 = 125/3

$$a_{42} = \frac{125}{3}$$

a43 = 85/2

$$a_{43} = \frac{85}{2}$$

a44 = 130/3

$$a_{44} = \frac{130}{3}$$

a45 = 265/6

$$a_{45} = \frac{265}{6}$$

a46 = 45

$$a_{46} = 45$$

a47 = 275/6

$$a_{47} = \frac{275}{6}$$

a48 = 140/3

$$a_{48} = \frac{140}{3}$$

a49 = 95/2

$$a_{49} = \frac{95}{2}$$

a50 = 145/3

$$a_{50} = \frac{145}{3}$$

a51 = 295/6

$$a_{51} = \frac{295}{6}$$

a52 = 50

$$a_{52} = 50$$

a53 = 305/6

$$a_{53} = \frac{305}{6}$$

a54 = 155/3

$$a_{54} = \frac{155}{3}$$

a55 = 105/2

$$a_{55} = \frac{105}{2}$$

...

n-член

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

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

a_55 = 105/2

$$a_{55} = \frac{105}{2}$$

Первый член

a_1 = 15/2

$$a_{1} = \frac{15}{2}$$