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(B) The number of ancestors in each generation forms a geometric progression: $2, 4, 8, \dots$ Here,the first term $a = 2$,the common ratio $r = 2$,an

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$2046$

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(B) The number of ancestors in each generation forms a geometric progression: $2, 4, 8, \dots$ Here,the first term $a = 2$,the common ratio $r = 2$,and the number of generations $n = 10$. Using the sum formula for a geometric progression: $S_{n} = \frac{a(r^{n} - 1)}{r - 1}$. Substituting the values: $S_{10} = \frac{2(2^{10} - 1)}{2 - 1}$. $S_{10} = 2(1024 - 1) = 2 	imes 1023 = 2046$. Thus,the total number of ancestors is $2046$.

$A$ person has $2$ parents,$4$ grandparents,$8$ great-grandparents,and so on. Find the total number of his ancestors during the $10$ generations preceding his own.

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