Question

martin has 2 parents, 4 grandparents, 8 great - grandparents and so on. find the number of ancestors during the 8 ancestors preceding his own.
a. 450
b. 510
c. 505
d. 255

Explanation:

Step1: Identify geometric series parameters

The sequence of ancestors is a geometric series with first term $a=2$, common ratio $r=2$, and number of terms $n=8$.

Step2: Apply sum formula for geometric series

Use the sum formula $S_n = a\frac{r^n - 1}{r - 1}$
$$S_8 = 2\times\frac{2^8 - 1}{2 - 1}$$

Step3: Calculate the value

First compute $2^8=256$, then $256-1=255$, finally $2\times255=510$.

Answer:

B. 510