Answer:
From the first generation = 2 ancestors.
From the second generation = 4 ancestors or (2)^2 ancestors.
From the third generation = 8 ancestors or (2)^3 ancestors.
We can infer from the given data, each consecutive generation possesses twice the number of members.
The sum will be:
2 + 4 + 8 + 16 + ... + (2)^39
To evaluate the amount of ancestors, let's employ the formula for the summation of a geometric sequence.
(Geometric sequence shows the sequence of numbers that varies by a specific factor. This factor is specifically known as a ratio).
Formula for Geometric sequence:
S = (a1) × 1 - (r)^n
--------------------------
1 - r
Take:
S -> sum
a1 -> first member of a sequence
r -> ratio
n -> number of elements
In this question, our:
a1 = 2; r = 2; and n = 39
S = (2) × 1 - (2)^39
-------------------------
1 - 2
S = 1,099,511,627,777
