Прогрессии/ Арифметическая прогрессия/ Найдите первый член и разность арифметической прогрессии, если: x53=240; х55=260;

Задача Найдите первый член и раз ... , если: x53=240; х55=260; (на арифметическую прогрессию)

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Решение

Вы ввели [src]
Найдите первый член и разность арифметической прогрессии, если: x53=240; х55=260;
Найдено в тексте задачи:
Первый член: x1 = ?
n-член xn (n = 54 + 1 = 55)
Разность: d = ?
Другие члены: x53 = 240
x55 = 260
Пример: ?
Найти члены от 1 до 55
Решение [src]
    x_n - x_k
d = ---------
      n - k
d=−xk+xn−k+nd = \frac{- x_{k} + x_{n}}{- k + n}
x_1 = x_n + d*(-1 + n)
x1=d(n−1)+xnx_{1} = d \left(n - 1\right) + x_{n}
            (-1 + n)*(x_n - x_k)
x_1 = x_n - --------------------
                   n - k
x1=xn−(n−1)(−xk+xn)−k+nx_{1} = x_{n} - \frac{\left(n - 1\right) \left(- x_{k} + x_{n}\right)}{- k + n}
    x_55 - x_53
d = -----------
         2
d=−x53+x552d = \frac{- x_{53} + x_{55}}{2}
             x_55 - x_53   
x_1 = x_55 - -----------*53
                  2
x1=x55−−x53+x552⋅53x_{1} = x_{55} - \frac{- x_{53} + x_{55}}{2} \cdot 53
    260 - 240
d = ---------
        2
d=−240+2602d = \frac{-240 + 260}{2}
            260 - 240   
x_1 = 260 - ---------*54
                2
x1=(−1)−240+2602⋅54+260x_{1} = \left(-1\right) \frac{-240 + 260}{2} \cdot 54 + 260
d = 10
d=10d = 10
x_1 = -280
x1=−280x_{1} = -280
Пример [src]
...
Расширенный пример:
-280; -270; -260; -250; -240; -230; -220; -210; -200; -190; -180; -170; -160; -150; -140; -130; -120; -110; -100; -90; -80; -70; -60; -50; -40; -30; -20; -10; 0; 10; 20; 30; 40; 50; 60; 70; 80; 90; 100; 110; 120; 130; 140; 150; 160; 170; 180; 190; 200; 210; 220; 230; 240; 250; 260...
x1 = -280
x1=−280x_{1} = -280
x2 = -270
x2=−270x_{2} = -270
x3 = -260
x3=−260x_{3} = -260
x4 = -250
x4=−250x_{4} = -250
x5 = -240
x5=−240x_{5} = -240
x6 = -230
x6=−230x_{6} = -230
x7 = -220
x7=−220x_{7} = -220
x8 = -210
x8=−210x_{8} = -210
x9 = -200
x9=−200x_{9} = -200
x10 = -190
x10=−190x_{10} = -190
x11 = -180
x11=−180x_{11} = -180
x12 = -170
x12=−170x_{12} = -170
x13 = -160
x13=−160x_{13} = -160
x14 = -150
x14=−150x_{14} = -150
x15 = -140
x15=−140x_{15} = -140
x16 = -130
x16=−130x_{16} = -130
x17 = -120
x17=−120x_{17} = -120
x18 = -110
x18=−110x_{18} = -110
x19 = -100
x19=−100x_{19} = -100
x20 = -90
x20=−90x_{20} = -90
x21 = -80
x21=−80x_{21} = -80
x22 = -70
x22=−70x_{22} = -70
x23 = -60
x23=−60x_{23} = -60
x24 = -50
x24=−50x_{24} = -50
x25 = -40
x25=−40x_{25} = -40
x26 = -30
x26=−30x_{26} = -30
x27 = -20
x27=−20x_{27} = -20
x28 = -10
x28=−10x_{28} = -10
x29 = 0
x29=0x_{29} = 0
x30 = 10
x30=10x_{30} = 10
x31 = 20
x31=20x_{31} = 20
x32 = 30
x32=30x_{32} = 30
x33 = 40
x33=40x_{33} = 40
x34 = 50
x34=50x_{34} = 50
x35 = 60
x35=60x_{35} = 60
x36 = 70
x36=70x_{36} = 70
x37 = 80
x37=80x_{37} = 80
x38 = 90
x38=90x_{38} = 90
x39 = 100
x39=100x_{39} = 100
x40 = 110
x40=110x_{40} = 110
x41 = 120
x41=120x_{41} = 120
x42 = 130
x42=130x_{42} = 130
x43 = 140
x43=140x_{43} = 140
x44 = 150
x44=150x_{44} = 150
x45 = 160
x45=160x_{45} = 160
x46 = 170
x46=170x_{46} = 170
x47 = 180
x47=180x_{47} = 180
x48 = 190
x48=190x_{48} = 190
x49 = 200
x49=200x_{49} = 200
x50 = 210
x50=210x_{50} = 210
x51 = 220
x51=220x_{51} = 220
x52 = 230
x52=230x_{52} = 230
x53 = 240
x53=240x_{53} = 240
x54 = 250
x54=250x_{54} = 250
x55 = 260
x55=260x_{55} = 260
...
Разность [src]
d = 10
d=10d = 10
n-член [src]
x_n = x_1 + d*(-1 + n)
xn=d(n−1)+x1x_{n} = d \left(n - 1\right) + x_{1}
x_55 = 260
x55=260x_{55} = 260
Сумма [src]
    n*(x_1 + x_n)
S = -------------
          2
S=n(x1+xn)2S = \frac{n \left(x_{1} + x_{n}\right)}{2}
      55*(-280 + 260)
S55 = ---------------
             2
S55=55(−280+260)2S_{55} = \frac{55 \left(-280 + 260\right)}{2}
S55 = -550
S55=−550S_{55} = -550
Первый член [src]
x_1 = -280
x1=−280x_{1} = -280