a person has two parents four grandparents eight great grand

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

Solution

No. of grandparents =2 + 4 + 8 .....

Its geomterice series withcommon ratio, r = 4/2 = 2

fisrt term, a1 = 2

So, nth term = ar^n-1

6th generation : a6 = a1r^5 = 2*(2)^5 = 64

9th generation : a9 = a1r^8 = 2(2)^8 = 2^9 = 512