Question

Brian has 2 parents, 4 grandparents, 8 great-grandparents, and so on.

a. Write an explicit formula for the number of
ancestors Brian has in a generation if
he goes back to the nth generation.

b. Write a recursive formula for the number of
ancestors Brian has in a generation if
he goes back to the nth generation.

(PLEASE EXPLAIN WHY)

Answer 1

Answer: Assuming the ancestors are distinct (very unlikely), each generation is double the size of the following generation. So

15

generations back will be

2

15

=

32768

ancestors.