Question 737267: Hey, I am confused with this word problem in which I have to use arithmetic/geometric sequences.
How many ancestors from parents to great-great-great-great grandparents do you have?
Thank you! :)
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! You have
2 parents
4 grandparents (2*2 = 4)
8 great-grandparents (2*2*2 = 8 ... each generation going back doubles the previous count)
16 great-great-grandparents (2*2*2*2 = 16)
32 great-great-great-grandparents (2*2*2*2*2 = 32)
64 great-great-great-great-grandparents (2*2*2*2*2*2 = 64)
Add up the individual counts:
2+4+8+16+32+64 = 126 ancestors
Shortcut:
You can take the shortcut and sum the geometric sequence 1*2^(n-1) from n = 1 to n = 6 (since you're going back 6 generations), then subtract off 1 since you're not counting yourself as an ancestor (of you). You would use the formula below and plug in a = 1, r = 2 and n = 6
S = a*(1-r^(n+1))/(1-r)
S = 1*(1-2^(6+1))/(1-2)
S = 1*(1-2^7)/(1-2)
S = 1*(1-128)/(1-2)
S = 1*(-127)/(-1)
S = 127
So if you summed up 1, 2, 4, 8, 16, 32, 64, then you would get 127...BUT you are NOT including yourself in this ancestor list. So you subtract 1 to get 127 - 1 = 126
So either way, there are 126 ancestors total.
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