Question

ou have two parents, four grandparents, eight great-grandparents, and so forth. (a) If all your ancestors were distinct, what would be the total number of your ancestors for the past 39 generations (counting your parents' generation as number one)? (Hint: Use the formula for the sum of a geometric sequence.) (b) Assuming that each generation represents 25 years, how long (in years) is 39 generations? yr (c) The total number of people who have ever lived is approximately 100 billion, which equals 1011 people. Compare this fact with the answer to part (a). What can you deduce? (Select all that apply.) Some of my ancestors must not have had children. Some ancestors on different branches of the family tree must be the same. People have been living on earth for less than 1,100 years. There could not have been 39 generations in my line of ancestry.

Answer 1

Answer:

Part A:

$2^{40}-2\\=1.0995*10^{12} ancestors$

Part B:

Generations Age=25*39=975 years

Part C:

1. Some ancestors on different branches of the family tree must be the same.
2. There could not have been 39 generations in my line of ancestry.

Step-by-step explanation:

Given Data:

Two Parents, Four Grand Parents, Eight great Grand Parents.

Generation=39

Solution:

Part A:

From given data Following series is made:

$2+2^2+2^3+.........+2^{39}$

Now, Above series will become:

$2[1+2+2^2+......+2^{38}]$

From geometric Sequence:

$2[\frac{2^{38+1}-1}{2-1} ]$

$2^{40}-2\\=1.0995*10^{12} ancestors$

Part B:

Generations Age=years*Number of generations

Generations Age=25*39=975 years

Part C:

Number of people lived= 10^11

Ancestors=$1.0995*10^{12} ancestors$

$10^{11}$

It means ancestors are not distinct, it means:

1. Some ancestors on different branches of the family tree must be the same.
2. There could not have been 39 generations in my line of ancestry.