Question

Find the number of ancestors i.e. parents, grandparents, great grandparents and so on, that a person has during the ten generations preceding his own.

Answer 1

The number of ancestors are
2,4,8,16,

It is a G.P. since,

4/2= 2
8/4= 2

Common ratio = 2
First term = a = 2
& number of generations (n) = 10

We have to find the number of his ancestors during the ten
generations preceding his own,
i.e. S10

As r>1

Sum of n terms in GP = [a((r^n)) - 1]/(r-1)


i.e. Sn = a[r^n -1]/(r-1)



Putting values of a=2, r=2, & n=10

S10 = [2×((2^10)-1]/(2-1)
S10= 2×1023/1
S10 = 2046

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