Chapter 11.3, Problem 10CYU

To determine

Find the total number of dominoes Miranda used.

Answer to Problem 10CYU

1023 number of dominoes.

Explanation of Solution

Given:

Miranda arranges some rows of dominoes so that after she knocks over the first one, each domino knocks over two more dominoes when it falls. If there are ten rows, how many dominoes do Miranda use?

Concept Used: The general formula for sum of terms of a GP series is ${\text{S}}_{\text{n}}=\frac{a_1(1-r^n)}{1-r}$

First term is $a_1$ and r is the common ratio.

Calculation:

The information given $a_1=1;r=2,n=10$

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

Thus, total number of dominoes is 1023.