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zarkam21
 one year ago
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zarkam21
 one year ago
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SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1So, first you add 1. Then, you add 2. Then, add 4.

zarkam21
 one year ago
Best ResponseYou've already chosen the best response.0Okay so for number 4 the answer would be 25?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1\(a_1=3\) \(a_2=4\) \(a_3=6\) \(a_4=10\) \(a_5=18\) \(a_6=34\) and so forth... \(a_2=a_1+1\) \(a_3=a_2+2=(a_1+1)+2=a_1+3=a_1+1+2\) \(a_4=a_3+4=(a_1+3)+4=a_1+7=a_11+2(4)=a_11+2^{41}\) \(a_5=a_4+8=(a_1+7)+8=a_1+15=a_11+2(8)=a_11+2^{51}\) \(a_6=a_5+16=(a_1+15)+16=a_1+31=a_11+2(16)=a_11+2^{61}\) \(a_n=a_11+2^{n1}\)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1I played around a little bit, and derived the following formula for the sequence, just in case you need it.

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1and you can further simplify this, knowing that \(a_1=3\) \(a_n=2+2^{n1}\)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1And the number of marbles in any \(n\)th line is given by \(a_n\).

zarkam21
 one year ago
Best ResponseYou've already chosen the best response.0So for the 7th line, there will be 50?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.12+2\(^{71}\) 2+2\(^{6}\) 2+(2\(^{3}\))\(^2\) 2+8\(^2\) 2+64=66 this is a byhand calculation.

zarkam21
 one year ago
Best ResponseYou've already chosen the best response.0Oh okay I understand the pattern now,, thanks ! :]
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