Является ли число B членом геометрической прогрессии (bn)? Если да, то его номер:bn=7/9*3n-8, B=63
1 ответ:
Читайте также
Даже не знаю, как такое решать) Ну, попробуем...
![b_n=[a, b, c]\\b/a=c/b\\\\a_n=[a, b+8, c]\\b+8-a=c-b-8\\\\b_{n_2}=[a, b+8,c+64]\\(b+8)/a=(c+64)/(b+8)\\\\ a=16+2b - c\\c=b^2/a\\b+8=a(c+64)/(b+8)\\(b+8)^2=a(c+64)\\ca=b^2\\b^2+16b+64=b^2+64a\\16b+64-64a=0\\16(b+4-4a)=0\\b+4-4a=0\\b=4a-4\\\\4a-4+8-a=c-4a+4-8\\7a+8-c=0\\7a+8-b^2/a=0\\7a^2+8a-b^2=0\\7a^2+8a-(4a-4)^2=0\\7a^2+8a-(16a^2-32a+16)=0\\-9a^2+40a-16=0\\9a^2-40a+16=0\\a_1=4/9\\a_2=4.\\\\1) a=4\\b=12\\c=36.\\\\2) a=4/9\\b=16/9-4=-20/9\\c=100/9.](https://tex.z-dn.net/?f=b_n%3D%5Ba%2C+b%2C+c%5D%5C%5Cb%2Fa%3Dc%2Fb%5C%5C%5C%5Ca_n%3D%5Ba%2C+b%2B8%2C+c%5D%5C%5Cb%2B8-a%3Dc-b-8%5C%5C%5C%5Cb_%7Bn_2%7D%3D%5Ba%2C+b%2B8%2Cc%2B64%5D%5C%5C%28b%2B8%29%2Fa%3D%28c%2B64%29%2F%28b%2B8%29%5C%5C%5C%5C%0A%0Aa%3D16%2B2b+-+c%5C%5Cc%3Db%5E2%2Fa%5C%5Cb%2B8%3Da%28c%2B64%29%2F%28b%2B8%29%5C%5C%28b%2B8%29%5E2%3Da%28c%2B64%29%5C%5Cca%3Db%5E2%5C%5Cb%5E2%2B16b%2B64%3Db%5E2%2B64a%5C%5C16b%2B64-64a%3D0%5C%5C16%28b%2B4-4a%29%3D0%5C%5Cb%2B4-4a%3D0%5C%5Cb%3D4a-4%5C%5C%5C%5C4a-4%2B8-a%3Dc-4a%2B4-8%5C%5C7a%2B8-c%3D0%5C%5C7a%2B8-b%5E2%2Fa%3D0%5C%5C7a%5E2%2B8a-b%5E2%3D0%5C%5C7a%5E2%2B8a-%284a-4%29%5E2%3D0%5C%5C7a%5E2%2B8a-%2816a%5E2-32a%2B16%29%3D0%5C%5C-9a%5E2%2B40a-16%3D0%5C%5C9a%5E2-40a%2B16%3D0%5C%5Ca_1%3D4%2F9%5C%5Ca_2%3D4.%5C%5C%5C%5C1%29+a%3D4%5C%5Cb%3D12%5C%5Cc%3D36.%5C%5C%5C%5C2%29+a%3D4%2F9%5C%5Cb%3D16%2F9-4%3D-20%2F9%5C%5Cc%3D100%2F9.)
Ураааа, я решил!!!
Ответ: 4, 12, 36, либо
.
P. S. Если слишком мелко, то вот в полном размере: https://www.dropbox.com/s/1bm6arn0a0jpohf/latex.jpg?dl=0
Ураааа, я решил!!!
Ответ: 4, 12, 36, либо
P. S. Если слишком мелко, то вот в полном размере: https://www.dropbox.com/s/1bm6arn0a0jpohf/latex.jpg?dl=0