Сумма первых пятнадцати членов арифметическая прогрессии равна 225, а второй член равен 3. Тогда сумма 3 и 5 члена равна?
Ответы
Ответ дал:
3
сумма 15 членов равна ![a_1+d(15-1)=a_1+14d=225 a_1+d(15-1)=a_1+14d=225](https://tex.z-dn.net/?f=a_1%2Bd%2815-1%29%3Da_1%2B14d%3D225)
![a_2=a_1+d(2-1)=a_1+d=3 a_2=a_1+d(2-1)=a_1+d=3](https://tex.z-dn.net/?f=a_2%3Da_1%2Bd%282-1%29%3Da_1%2Bd%3D3)
получим и решим систему
![\left \{ {{a_1+14d=225} \atop{a_1+d=3}}\right.\\ \left\{{{3-d+14d=225}\atop {a_1=3-d}}\right.\\ \left \{{{13d=222}\atop{a_1=3-d}}\right.\\ \left \{ {{d=17 \frac{1}{13}}\atop{a_1=3-17\frac{1}{13}}}\right.\\ \left \{{{d=17\frac{1}{13} }\atop {a_1=-14\frac{1}{13}}}\right.\\a_3=a_1+d(3-1)=a_1+2d=-14\dfrac{1}{13}+2*17 \dfrac{1}{13}= \dfrac{261}{13}\\a_5=a_1+d(5-1)=a_1+4d=-14\dfrac{1}{13}+4*17 \frac{1}{13}=\dfrac{705}{13}\\a_1+a_5=\dfrac{261+705}{13}= \dfrac{966}{13}= 74\dfrac{4}{13} \left \{ {{a_1+14d=225} \atop{a_1+d=3}}\right.\\ \left\{{{3-d+14d=225}\atop {a_1=3-d}}\right.\\ \left \{{{13d=222}\atop{a_1=3-d}}\right.\\ \left \{ {{d=17 \frac{1}{13}}\atop{a_1=3-17\frac{1}{13}}}\right.\\ \left \{{{d=17\frac{1}{13} }\atop {a_1=-14\frac{1}{13}}}\right.\\a_3=a_1+d(3-1)=a_1+2d=-14\dfrac{1}{13}+2*17 \dfrac{1}{13}= \dfrac{261}{13}\\a_5=a_1+d(5-1)=a_1+4d=-14\dfrac{1}{13}+4*17 \frac{1}{13}=\dfrac{705}{13}\\a_1+a_5=\dfrac{261+705}{13}= \dfrac{966}{13}= 74\dfrac{4}{13}](https://tex.z-dn.net/?f=+%5Cleft+%5C%7B+%7B%7Ba_1%2B14d%3D225%7D+%5Catop%7Ba_1%2Bd%3D3%7D%7D%5Cright.%5C%5C+%5Cleft%5C%7B%7B%7B3-d%2B14d%3D225%7D%5Catop+%7Ba_1%3D3-d%7D%7D%5Cright.%5C%5C+%5Cleft+%5C%7B%7B%7B13d%3D222%7D%5Catop%7Ba_1%3D3-d%7D%7D%5Cright.%5C%5C+%5Cleft+%5C%7B+%7B%7Bd%3D17+%5Cfrac%7B1%7D%7B13%7D%7D%5Catop%7Ba_1%3D3-17%5Cfrac%7B1%7D%7B13%7D%7D%7D%5Cright.%5C%5C+%5Cleft+%5C%7B%7B%7Bd%3D17%5Cfrac%7B1%7D%7B13%7D+%7D%5Catop+%7Ba_1%3D-14%5Cfrac%7B1%7D%7B13%7D%7D%7D%5Cright.%5C%5Ca_3%3Da_1%2Bd%283-1%29%3Da_1%2B2d%3D-14%5Cdfrac%7B1%7D%7B13%7D%2B2%2A17+%5Cdfrac%7B1%7D%7B13%7D%3D+%5Cdfrac%7B261%7D%7B13%7D%5C%5Ca_5%3Da_1%2Bd%285-1%29%3Da_1%2B4d%3D-14%5Cdfrac%7B1%7D%7B13%7D%2B4%2A17+%5Cfrac%7B1%7D%7B13%7D%3D%5Cdfrac%7B705%7D%7B13%7D%5C%5Ca_1%2Ba_5%3D%5Cdfrac%7B261%2B705%7D%7B13%7D%3D+%5Cdfrac%7B966%7D%7B13%7D%3D++74%5Cdfrac%7B4%7D%7B13%7D+)
получим и решим систему
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