Question

A person has $2$ parents, $4$grandparents, and so on. Find the numbers of his ancestors during the ten-generation preceding his own.

Answer 1

Step 1: Analysing the problem statement

Number of ancestors during the ten generations preceding his own generation

Sum of $10$ terms of the GP $2,4,8,...$

Here, $a=2,r=2,n=10$

Step 2: Sum of 10 generations

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

Substituting the given values,

$2\left[\frac{2^{10}-1}{2-1}\right]=2046$

Therefore, $S_{10}=2046$