A person has 2 parents, 4 grandparents, 8 great grandparents, and so on.

Question:

A person has 2 parents, 4 grandparents, 8 great grandparents, and so on. Find the number of his ancestors during the ten generations preceding his own.

Solution:

Here, the ancestors of the person form the G.P.  2, 4, 8, 16, ........

Now, first term, = 2

And,  r = 2

∴ Number of  his ancestors during the ten generations preceding his own,

$S_{10}=2\left(\frac{2^{10}-1}{2-1}\right)=2(1024-1)=2046$