Dane is participating in a reading challenge and wants to read more each day than the day before. Dane reads 10 pages on the 1st day, 19 pages on the 2nd day, 28 pages on the 3rd day, and so on. Assume the pattern continues. How many pages will Dane read on the 29 th day?

Answer 1

To analyze the pattern of pages Dane reads each day, we first note the number of pages read:

• Day 1: 10 pages
• Day 2: 19 pages
• Day 3: 28 pages

Next, we calculate the difference in pages read from one day to the next:

• Difference between Day 2 and Day 1: \(19 - 10 = 9\)
• Difference between Day 3 and Day 2: \(28 - 19 = 9\)

The difference remains constant at 9 pages. Therefore, it seems that Dane reads 9 more pages each day than the previous day.

Now, we can express the number of pages read on the \(n\)-th day with the following formula:

\[ \text{Pages on Day } n = 10 + (n - 1) \times 9 \]

Simplifying further:

\[ \text{Pages on Day } n = 10 + 9n - 9 = 9n + 1 \]

We can check our formula with known values:

• For Day 1: \[ 9(1) + 1 = 9 + 1 = 10 \text{ pages} \]

• For Day 2: \[ 9(2) + 1 = 18 + 1 = 19 \text{ pages} \]

• For Day 3: \[ 9(3) + 1 = 27 + 1 = 28 \text{ pages} \]

The formula holds true. Now, we need to find the number of pages Dane will read on the 29th day:

\[ \text{Pages on Day 29} = 9(29) + 1 \]

Calculating this:

\[ 9(29) = 261 \] \[ 261 + 1 = 262 \]

Thus, Dane will read 262 pages on the 29th day.