Question

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

Answer 1

The number of ancestors are 2, 4, 8, 16....it is in GP common ratio = r = \(\frac{4}{2}\) = 2a = 2 and n = 10 

Sum of GP for n terms = \(\frac{a(r^n-1)}{r-1}\)

⇒ a = 2, r = 2, n = 10

∴ Substituting the above values in (1) we get

⇒ \(\cfrac{2(2^{10} - 1)} {2-1}\)

⇒ 2(1024 - 1) 

⇒ 2(1023) 

⇒ 2046