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.

• A. $2042$
• B. $2046$
• C. $2044$
• D. $2045$

Answer 1

Answer: (B)

$2046$

Answer 2

Here $a = 2, r = 2$ and $n = 10$ $\therefore S_{n} = \frac{a\left(r^{n}-1\right)}{r-1}$ $\Rightarrow S_{10} = 2\left(2^{10}-1\right)$ $= 2046$ Hence, the number of ancestors preceding the person is $2046$.