A person has 2 parents, 4 grandparents, 8 great grandparents, and so on. number of his ancestors dur

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8. Sequences and Series

easy

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

$2046$

B

$2046$

C

$2046$

D

$2046$

Solution

Here $a=2, r=2$ and $n=10$

Using the sum formula $S_{n}=\frac{a\left(r^{n}-1\right)}{r-1}$

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

Hence, the number of ancestors preceding the person is $2046$

Standard 11

Mathematics

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