Задача S41, если a1=0;d=1,5 (на арифметическую прогрессию)

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S41, если a1=0;d=1,5

Найдено в тексте задачи:

Первый член: a1 = 0

n-член an (n = 40 + 1 = 41)

Разность: d = (3/2)

Другие члены: a1 = 0

Пример: ?

Найти члены от 1 до 41

Первый член

a_1 = 0

$$a_{1} = 0$$

Разность

d = 3/2

$$d = \frac{3}{2}$$

Сумма

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

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

S41 = 1230

$$S_{41} = 1230$$

n-член

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

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

a_41 = 60

$$a_{41} = 60$$

Пример

...

Расширенный пример:

0; 3/2; 3; 9/2; 6; 15/2; 9; 21/2; 12; 27/2; 15; 33/2; 18; 39/2; 21; 45/2; 24; 51/2; 27; 57/2; 30; 63/2; 33; 69/2; 36; 75/2; 39; 81/2; 42; 87/2; 45; 93/2; 48; 99/2; 51; 105/2; 54; 111/2; 57; 117/2; 60...

a1 = 0

$$a_{1} = 0$$

a2 = 3/2

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

a3 = 3

$$a_{3} = 3$$

a4 = 9/2

$$a_{4} = \frac{9}{2}$$

a5 = 6

$$a_{5} = 6$$

a6 = 15/2

$$a_{6} = \frac{15}{2}$$

a7 = 9

$$a_{7} = 9$$

a8 = 21/2

$$a_{8} = \frac{21}{2}$$

a9 = 12

$$a_{9} = 12$$

a10 = 27/2

$$a_{10} = \frac{27}{2}$$

a11 = 15

$$a_{11} = 15$$

a12 = 33/2

$$a_{12} = \frac{33}{2}$$

a13 = 18

$$a_{13} = 18$$

a14 = 39/2

$$a_{14} = \frac{39}{2}$$

a15 = 21

$$a_{15} = 21$$

a16 = 45/2

$$a_{16} = \frac{45}{2}$$

a17 = 24

$$a_{17} = 24$$

a18 = 51/2

$$a_{18} = \frac{51}{2}$$

a19 = 27

$$a_{19} = 27$$

a20 = 57/2

$$a_{20} = \frac{57}{2}$$

a21 = 30

$$a_{21} = 30$$

a22 = 63/2

$$a_{22} = \frac{63}{2}$$

a23 = 33

$$a_{23} = 33$$

a24 = 69/2

$$a_{24} = \frac{69}{2}$$

a25 = 36

$$a_{25} = 36$$

a26 = 75/2

$$a_{26} = \frac{75}{2}$$

a27 = 39

$$a_{27} = 39$$

a28 = 81/2

$$a_{28} = \frac{81}{2}$$

a29 = 42

$$a_{29} = 42$$

a30 = 87/2

$$a_{30} = \frac{87}{2}$$

a31 = 45

$$a_{31} = 45$$

a32 = 93/2

$$a_{32} = \frac{93}{2}$$

a33 = 48

$$a_{33} = 48$$

a34 = 99/2

$$a_{34} = \frac{99}{2}$$

a35 = 51

$$a_{35} = 51$$

a36 = 105/2

$$a_{36} = \frac{105}{2}$$

a37 = 54

$$a_{37} = 54$$

a38 = 111/2

$$a_{38} = \frac{111}{2}$$

a39 = 57

$$a_{39} = 57$$

a40 = 117/2

$$a_{40} = \frac{117}{2}$$

a41 = 60

$$a_{41} = 60$$

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