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

Question

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 (A) 1084 (B) 2046 (C) 2250 (D) 1024

Tardigrade Admin · Accepted Answer

Here, a=2, r=2 and n=10 Since, Sn=(a(rn-1)/r-1) We have, S10=(2(210-1)/2-1) =2(1024-1) =2 × 1023=2046 Hence, the number of ancestors preceding the person is 2046.

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

1084

2046

2250

1024

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

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

1084

2046

2250

1024

Here, a=2,r=2 and n=10 Since, Sn​=r−1a(rn−1)​ We have, S10​=2−12(210−1)​ =2(1024−1) =2×1023=2046 Hence, the number of ancestors preceding the person is 2046.

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