Question

Which of the following is the total number of pennies on Rows 1-4 (the first 32 squares)? 232 – 1 232 232 1.

Answer 1

The total number of pennies on Rows 1-4 (the first 32 squares) is 4,294,967,295 or 2³².

What is geometric progression?

A geometric progression is the series of numbers such that the ratio of any two consecutive numbers of the series is the same.

If we look closely at the problem we will understand that on each of the square boxes the number of pennies will get double from the previous one therefore, we can say that it is forming a geometric progression where the first term of the sequence is 1, while the common ratio is of 2. thus,

The total number of pennies on Rows 1-4 (the first 32 squares) is the sum of the geometric progression for the first 32, terms, therefore,

$S_n = a_1(\dfrac{r^n-1}{r-1})$

Now, as we know that the first term of the series is 1, while the common ratio(r) is 2, and the number of terms(n=32). Thus, the sum can be written as,

$S_n = a_1(\dfrac{r^n-1}{r-1})\\\\S_n = 1(\dfrac{2^{32}-1}{2-1})\\\\S_n = 4,294,967,295$

The number can also be written as,

$S_n = 4,294,967,295\\\\S_n = 2^{32}$

Hence, the total number of pennies on Rows 1-4 (the first 32 squares) is 4,294,967,295 or 2³².

Learn more about Geometric progression:

brainly.com/question/14320920

Answer 2

Answer:

A: 2^32 – 1

Step-by-step explanation: