В арифметической прогрессии каждый последующий член
![a_{n+1}](https://tex.z-dn.net/?f=a_%7Bn%2B1%7D)
получается из предыдущего
![a_{n}](https://tex.z-dn.net/?f=a_%7Bn%7D)
путём прибавления к нему одного и того же числа
![d](https://tex.z-dn.net/?f=d)
, называемого разностью арифм. прогрессии:
![a_{n+1}=a_{n}+d](https://tex.z-dn.net/?f=a_%7Bn%2B1%7D%3Da_%7Bn%7D%2Bd)
.
Можно выразить n-ый член арифм. прогрессии через первый:
![a_1\\a_2=a_1+d\\a_3=a_2+d=(a_1+d)+d=a_1+2d\\a_4=a_3+d=(a_1+2d)+d=a_1+3d\\..........................................................................................\\a_{n}=a_{n-1}+d=(a_1+(n-2)\cdot d)+d=a_1+(n-1)\cdot d\\a_{n+1}=a_{n}+d=(a_1+(n-1)\cdot d)+d=a_1+n\cdot d\\...........................................................................................](https://tex.z-dn.net/?f=a_1%5C%5Ca_2%3Da_1%2Bd%5C%5Ca_3%3Da_2%2Bd%3D%28a_1%2Bd%29%2Bd%3Da_1%2B2d%5C%5Ca_4%3Da_3%2Bd%3D%28a_1%2B2d%29%2Bd%3Da_1%2B3d%5C%5C..........................................................................................%5C%5Ca_%7Bn%7D%3Da_%7Bn-1%7D%2Bd%3D%28a_1%2B%28n-2%29%5Ccdot+d%29%2Bd%3Da_1%2B%28n-1%29%5Ccdot+d%5C%5Ca_%7Bn%2B1%7D%3Da_%7Bn%7D%2Bd%3D%28a_1%2B%28n-1%29%5Ccdot+d%29%2Bd%3Da_1%2Bn%5Ccdot+d%5C%5C...........................................................................................)
В примере выражают 5-ый, 2-ой и 4-ый члены арифм. прогрессии
через 1-ый:
![a_5=a_1+4d\; ,\; \; a_2=a_1+d\; ,\; \; a_4=a_1+3d\\\\ \left \{ {{a_1+a_5=14} \atop {a_2\cdot a_4=45}} \right. \; \; \left \{ {{a_1+(a_1+4d)=14} \atop {(a_1+d)\cdot (a_1+3d)=45}} \right. \; \; \left \{ {{2a_1+4d=14} \atop {a_1^2+4a_1d+3d^2=45}} \right. \; \left \{ {{a_1+2d=7} \atop {a_1^2+4a_1d+3d^2=45}} \right. \\\\ \left \{ {{a_1=7-2d} \atop {(7-2d)^2+4(7-2d)\cdot d+3d^2=45}} \right. \; \; \left \{ {{a_1=7-2d} \atop {4-d^2=0}} \right. \\\\4-d^2=0\; ,\; \; d^2=4\; \; ,\; \; d=\pm 2](https://tex.z-dn.net/?f=a_5%3Da_1%2B4d%5C%3B+%2C%5C%3B+%5C%3B+a_2%3Da_1%2Bd%5C%3B+%2C%5C%3B+%5C%3B+a_4%3Da_1%2B3d%5C%5C%5C%5C+%5Cleft+%5C%7B+%7B%7Ba_1%2Ba_5%3D14%7D+%5Catop+%7Ba_2%5Ccdot+a_4%3D45%7D%7D+%5Cright.++%5C%3B+%5C%3B+%5Cleft+%5C%7B+%7B%7Ba_1%2B%28a_1%2B4d%29%3D14%7D+%5Catop+%7B%28a_1%2Bd%29%5Ccdot+%28a_1%2B3d%29%3D45%7D%7D+%5Cright.+%5C%3B+%5C%3B++%5Cleft+%5C%7B+%7B%7B2a_1%2B4d%3D14%7D+%5Catop+%7Ba_1%5E2%2B4a_1d%2B3d%5E2%3D45%7D%7D+%5Cright.+%5C%3B++%5Cleft+%5C%7B+%7B%7Ba_1%2B2d%3D7%7D+%5Catop+%7Ba_1%5E2%2B4a_1d%2B3d%5E2%3D45%7D%7D+%5Cright.+%5C%5C%5C%5C+%5Cleft+%5C%7B+%7B%7Ba_1%3D7-2d%7D+%5Catop+%7B%287-2d%29%5E2%2B4%287-2d%29%5Ccdot+d%2B3d%5E2%3D45%7D%7D+%5Cright.+%5C%3B+%5C%3B++%5Cleft+%5C%7B+%7B%7Ba_1%3D7-2d%7D+%5Catop+%7B4-d%5E2%3D0%7D%7D+%5Cright.+%5C%5C%5C%5C4-d%5E2%3D0%5C%3B+%2C%5C%3B+%5C%3B+d%5E2%3D4%5C%3B+%5C%3B+%2C%5C%3B+%5C%3B+d%3D%5Cpm+2)
![d_1=-2\; \; \to \; \; a_1^{(1)}=7-2\cdot (-2)=11\\\\d_2=2\; \; \to \; \; a_1^{(2)}=7-2\cdot 2=3\\\\Otvet:\; \; a_1=11\; ,\; d=-2\; \; ili\; \; a_1=3\; ,\; d=2\; .](https://tex.z-dn.net/?f=d_1%3D-2%5C%3B+%5C%3B+%5Cto+%5C%3B+%5C%3B+a_1%5E%7B%281%29%7D%3D7-2%5Ccdot+%28-2%29%3D11%5C%5C%5C%5Cd_2%3D2%5C%3B+%5C%3B+%5Cto+%5C%3B+%5C%3B+a_1%5E%7B%282%29%7D%3D7-2%5Ccdot+2%3D3%5C%5C%5C%5COtvet%3A%5C%3B+%5C%3B+a_1%3D11%5C%3B+%2C%5C%3B+d%3D-2%5C%3B+%5C%3B+ili%5C%3B+%5C%3B+a_1%3D3%5C%3B+%2C%5C%3B+d%3D2%5C%3B+.)
45:1 1/2=45:1,5=30ч-время второго
1:45=1/45 в час делает 1
1:30=1/30 в час делает 2
1/45+1/30=2/90+3/90=5/90=1/18-делают в час вместе
1:1/18=18ч- сделают задание вместе
Х вполне может быть равен 2, а у-1.
Все сходится-
2*2+1=5
<span>1)
Дано: Решение: b2=0.5*(-128) = -64
b1=-128 b3=0.5*(-64) = -32
bn+1=1/2bn b4=0.5*(-32)=-16
Найти: b5=0.5*(-16)=-8
b5
Ответ: b5=-2</span>