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)

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 $2046$.