Chapter 11.3, Problem 1CYU

To determine

Find the number of ancestors would there be.

Answer to Problem 1CYU

Number of ancestors is 2046.

Explanation of Solution

Given:

Dean is making a family tree for his grandfather. He was able to trace many generations. If Dean could trace his family back 10 generations, starting with his parents how many ancestors would there be?

Concept Used:

As Dean could trace his family back 10 generations, starting with his parents,

We have that $a_1=2;r=2;n=10$

Now we have to find ${\text{S}}_{\text{n}}$ by using the formula ${\text{S}}_{\text{n}}=\frac{a_1(1-r^n)}{1-r}$

Calculation:

Now we have to find ${\text{S}}_{\text{n}}$ by using the formula ${\text{S}}_{\text{n}}=\frac{a_1(1-r^n)}{1-r}$

  $\begin{array}{l}{a}_1=2;r=2;n=10;\text{find}{\text{S}}_{\text{n}}\\ {\text{S}}_{\text{n}}=\frac{a_1(1-r^n)}{1-r}\\ {\text{S}}_{10}=\frac{2(1-2^{10})}{1-2}=\frac{2(1-1024)}{-1}=\frac{2(-1023)}{-1}=2046\end{array}$

Thus, the number of ancestors is 2046.