Charlotte read 10 pages of a storybook on the first day. She read 15 pages of the same storybook on the second day, 20 pages on the third day and so on. How many pages had the storybook if Charlotte finished it on the eight day?
pages on day n = 10 + 5(n-1)
google the words:
arithmetic sequence math is fun
look for sum of sequence terms one through eight
If she can do it, each day increases by 5.
10 + 15 + 20 + 25 + 30 + 35 + 40 + 45 = ?
I guess the problem should have asked for terms 1 through 999 :)
To find out how many pages the storybook had, we need to determine the pattern in the number of pages Charlotte read each day. From the given information, we can observe that the number of pages she read increases by 5 each day.
On the first day, Charlotte read 10 pages.
On the second day, she read 10 + 5 = 15 pages.
On the third day, she read 15 + 5 = 20 pages.
And so on.
To find out how many pages she read on the eighth day, we can use the formula for the nth term of an arithmetic sequence:
aₙ = a₁ + (n - 1)d
where:
aₙ is the nth term (number of pages read on the nth day)
a₁ is the first term (number of pages read on the first day)
n is the number of terms (number of days)
d is the common difference (in this case, 5 since the number of pages increases by 5 each day)
Using the formula, we can calculate the number of pages Charlotte read on the eighth day:
a₈ = 10 + (8 - 1) * 5
a₈ = 10 + 7 * 5
a₈ = 10 + 35
a₈ = 45
Therefore, Charlotte read 45 pages on the eighth day. However, we need to find out how many pages the storybook had in total.
To calculate the total number of pages, we need to find the sum of the arithmetic sequence. The formula for the sum of an arithmetic sequence is:
Sₙ = (n/2)(a₁ + aₙ)
where:
Sₙ is the sum of the sequence (total number of pages read)
n is the number of terms (number of days)
a₁ is the first term (number of pages read on the first day)
aₙ is the nth term (number of pages read on the nth day)
Using the formula, we can calculate the total number of pages:
S₈ = (8/2)(10 + 45)
S₈ = 4 * 55
S₈ = 220
Therefore, the storybook had a total of 220 pages if Charlotte finished it on the eighth day.