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windsylph
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Find a solution to the sequence 2, 14, 86, 518, 3110, ... . In other words, find a closed form of the recursive function a_n = 6a_{n1} + 2.
 2 years ago
 2 years ago
windsylph Group Title
Find a solution to the sequence 2, 14, 86, 518, 3110, ... . In other words, find a closed form of the recursive function a_n = 6a_{n1} + 2.
 2 years ago
 2 years ago

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King Group TitleBest ResponseYou've already chosen the best response.1
the sequence is as follows: 142=12 8614=12*6 51886=12*6*6 and so on......
 2 years ago

Zarkon Group TitleBest ResponseYou've already chosen the best response.0
for ones like this I usually work my way backwards \[a_n = 6a_{n1} + 2=6(6a_{n2}+2)+2=6^2a_{n2}+6\cdot 2+2\] \[=6^2(6a_{n3}+2)+6\cdot 2+2=6^3a_{n3}+6^2\cdot 2+6\cdot 2+2=\cdots\]
 2 years ago

FoolAroundMath Group TitleBest ResponseYou've already chosen the best response.0
\[a_{n} = 6^{n1}a_{n(n1)}+6^{n2}.2+...+6.2+2\] \[a_{n} = 6^{n1}.2 + 6^{n2}.2 + ... + 6.2 + 6^{0}.2\] \[a_{n} = 2\frac{6^{n}1}{61}\]
 2 years ago
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