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

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

Sequences and Series

Solution:

Here, $a=2, r=2$ and $n=10$
Since, $ S_n=\frac{a\left(r^n-1\right)}{r-1}$
We have, $ S_{10}=\frac{2\left(2^{10}-1\right)}{2-1}$
$=2(1024-1)$
$=2 \times 1023=2046$
Hence, the number of ancestors preceding the person is 2046.