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Q.
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.
Sequences and Series
Solution:
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 $2046$.