Задача Найди разность арифметиче ... есии если a43=86 a95=190 (на арифметическую прогрессию)

Вы ввели

найди разность арифметической прогресии если
a43=86 a95=190

Найдено в тексте задачи:

Первый член: a1 = ?

n-член an (n = 94 + 1 = 95)

Разность: d = ?

Другие члены: a43 = 86
a95 = 190

Пример: ?

Найти члены от 1 до 95

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_95 - a_43
d = -----------
         52    

$$d = \frac{- a_{43} + a_{95}}{52}$$

             a_95 - a_43   
a_1 = a_95 - -----------*93
                  52       

$$a_{1} = a_{95} - \frac{- a_{43} + a_{95}}{52} \cdot 93$$

    190 - 86
d = --------
       52   

$$d = \frac{-86 + 190}{52}$$

            190 - 86   
a_1 = 190 - --------*94
               52      

$$a_{1} = \left(-1\right) \frac{-86 + 190}{52} \cdot 94 + 190$$

d = 2

$$d = 2$$

a_1 = 2

$$a_{1} = 2$$

Первый член

a_1 = 2

$$a_{1} = 2$$

Разность

d = 2

$$d = 2$$

n-член

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

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

a_95 = 190

$$a_{95} = 190$$

Сумма

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

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

      95*(2 + 190)
S95 = ------------
           2      

$$S_{95} = \frac{95 \cdot \left(2 + 190\right)}{2}$$

S95 = 9120

$$S_{95} = 9120$$

Пример

...

Расширенный пример:

2; 4; 6; 8; 10; 12; 14; 16; 18; 20; 22; 24; 26; 28; 30; 32; 34; 36; 38; 40; 42; 44; 46; 48; 50; 52; 54; 56; 58; 60; 62; 64; 66; 68; 70; 72; 74; 76; 78; 80; 82; 84; 86; 88; 90; 92; 94; 96; 98; 100; 102; 104; 106; 108; 110; 112; 114; 116; 118; 120; 122; 124; 126; 128; 130; 132; 134; 136; 138; 140; 142; 144; 146; 148; 150; 152; 154; 156; 158; 160; 162; 164; 166; 168; 170; 172; 174; 176; 178; 180; 182; 184; 186; 188; 190...

a1 = 2

$$a_{1} = 2$$

a2 = 4

$$a_{2} = 4$$

a3 = 6

$$a_{3} = 6$$

a4 = 8

$$a_{4} = 8$$

a5 = 10

$$a_{5} = 10$$

a6 = 12

$$a_{6} = 12$$

a7 = 14

$$a_{7} = 14$$

a8 = 16

$$a_{8} = 16$$

a9 = 18

$$a_{9} = 18$$

a10 = 20

$$a_{10} = 20$$

a11 = 22

$$a_{11} = 22$$

a12 = 24

$$a_{12} = 24$$

a13 = 26

$$a_{13} = 26$$

a14 = 28

$$a_{14} = 28$$

a15 = 30

$$a_{15} = 30$$

a16 = 32

$$a_{16} = 32$$

a17 = 34

$$a_{17} = 34$$

a18 = 36

$$a_{18} = 36$$

a19 = 38

$$a_{19} = 38$$

a20 = 40

$$a_{20} = 40$$

a21 = 42

$$a_{21} = 42$$

a22 = 44

$$a_{22} = 44$$

a23 = 46

$$a_{23} = 46$$

a24 = 48

$$a_{24} = 48$$

a25 = 50

$$a_{25} = 50$$

a26 = 52

$$a_{26} = 52$$

a27 = 54

$$a_{27} = 54$$

a28 = 56

$$a_{28} = 56$$

a29 = 58

$$a_{29} = 58$$

a30 = 60

$$a_{30} = 60$$

a31 = 62

$$a_{31} = 62$$

a32 = 64

$$a_{32} = 64$$

a33 = 66

$$a_{33} = 66$$

a34 = 68

$$a_{34} = 68$$

a35 = 70

$$a_{35} = 70$$

a36 = 72

$$a_{36} = 72$$

a37 = 74

$$a_{37} = 74$$

a38 = 76

$$a_{38} = 76$$

a39 = 78

$$a_{39} = 78$$

a40 = 80

$$a_{40} = 80$$

a41 = 82

$$a_{41} = 82$$

a42 = 84

$$a_{42} = 84$$

a43 = 86

$$a_{43} = 86$$

a44 = 88

$$a_{44} = 88$$

a45 = 90

$$a_{45} = 90$$

a46 = 92

$$a_{46} = 92$$

a47 = 94

$$a_{47} = 94$$

a48 = 96

$$a_{48} = 96$$

a49 = 98

$$a_{49} = 98$$

a50 = 100

$$a_{50} = 100$$

a51 = 102

$$a_{51} = 102$$

a52 = 104

$$a_{52} = 104$$

a53 = 106

$$a_{53} = 106$$

a54 = 108

$$a_{54} = 108$$

a55 = 110

$$a_{55} = 110$$

a56 = 112

$$a_{56} = 112$$

a57 = 114

$$a_{57} = 114$$

a58 = 116

$$a_{58} = 116$$

a59 = 118

$$a_{59} = 118$$

a60 = 120

$$a_{60} = 120$$

a61 = 122

$$a_{61} = 122$$

a62 = 124

$$a_{62} = 124$$

a63 = 126

$$a_{63} = 126$$

a64 = 128

$$a_{64} = 128$$

a65 = 130

$$a_{65} = 130$$

a66 = 132

$$a_{66} = 132$$

a67 = 134

$$a_{67} = 134$$

a68 = 136

$$a_{68} = 136$$

a69 = 138

$$a_{69} = 138$$

a70 = 140

$$a_{70} = 140$$

a71 = 142

$$a_{71} = 142$$

a72 = 144

$$a_{72} = 144$$

a73 = 146

$$a_{73} = 146$$

a74 = 148

$$a_{74} = 148$$

a75 = 150

$$a_{75} = 150$$

a76 = 152

$$a_{76} = 152$$

a77 = 154

$$a_{77} = 154$$

a78 = 156

$$a_{78} = 156$$

a79 = 158

$$a_{79} = 158$$

a80 = 160

$$a_{80} = 160$$

a81 = 162

$$a_{81} = 162$$

a82 = 164

$$a_{82} = 164$$

a83 = 166

$$a_{83} = 166$$

a84 = 168

$$a_{84} = 168$$

a85 = 170

$$a_{85} = 170$$

a86 = 172

$$a_{86} = 172$$

a87 = 174

$$a_{87} = 174$$

a88 = 176

$$a_{88} = 176$$

a89 = 178

$$a_{89} = 178$$

a90 = 180

$$a_{90} = 180$$

a91 = 182

$$a_{91} = 182$$

a92 = 184

$$a_{92} = 184$$

a93 = 186

$$a_{93} = 186$$

a94 = 188

$$a_{94} = 188$$

a95 = 190

$$a_{95} = 190$$

...