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Annette [7]
3 years ago
14

You have two parents, four grandparents, eight great-grandparents, and so forth. (a) If all your ancestors were distinct, what w

ould be the total number of your ancestors for the past 39 generations (counting your parents' generation as number one)
Social Studies
1 answer:
s2008m [1.1K]3 years ago
4 0

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

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