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(C) The number of ancestors in each generation forms a Geometric Progression $(G.P.)$: $2, 4, 8, \ldots$ up to $10$ terms.Here,the first term $a = 2$

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$2046$

Vedclass · Answer

(C) The number of ancestors in each generation forms a Geometric Progression $(G.P.)$: $2, 4, 8, \ldots$ up to $10$ terms.Here,the first term $a = 2$ and the common ratio $r = 2$.The sum of the first $n$ terms of a $G.P.$ is given by the formula: $S_n = a(r^n - 1) / (r - 1)$.For $n = 10$ generations,the total number of ancestors is:$S_{10} = 2(2^{10} - 1) / (2 - 1)$$S_{10} = 2(1024 - 1) / 1$$S_{10} = 2 	imes 1023 = 2046$.Therefore,the total number of ancestors up to the $10^{th}$ generation is $2046$.

$A$ person has two parents (father and mother),four grandparents,eight great-grandparents,and so on. Find the total number of ancestors the person has up to the $10^{th}$ generation.

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