Question

Each person has two parents, four grandparents, eight great-grandparents, and so on. What is the total number of ancestors a person has, going back five generations? twelve generations?

Answer 1

62

8190

1) Gathering the data:

So Adding the 2 + 4 +8 +16+32 Then we can write that up to the 5th generation each person has 62 ancestors.

2) Or we can check. Let's write out considering that the ratio is 2 and the first term is 2 since the person per se is not counted.

`\begin{gathered} S=(a_1(1-r^n))/(1-r) \\ S_5=\text{ }(2(1-2^5)^(\square))/(1-2)=62 \\ S_(12)=(2(1-2^(11)))/(1-2)=8190 \end{gathered}`

3) Hence, each person has counting back up to the 5th generations 62 ancestors and 4094 when it comes to 11 generations