Answer:
Explanation:
On the first day, Ms. Dubacek gave 6 new spelling words.
On each subsequent day, she gave an additional 3 new spelling words.
Therefore, on the second day of school, she gave a total of 6 + 3 = 9 new spelling words.
On the third day of school, she gave a total of 6 + 3 + 3 = 12 new spelling words.
We can see a pattern emerging here: on each day, she gives 6 more words than the previous day.
So on the 21st day of school, she will have given a total of:
6 + (9 + 12 + 15 + ... + 60)
To find the sum of this arithmetic series, we can use the formula:
S = n/2 * (a + l)
where:
S = the sum of the series
n = the number of terms in the series
a = the first term in the series
l = the last term in the series
In this case, we have:
n = 19 (since we're counting from the second day of school to the 21st day)
a = 9 (since that was the total number of spelling words given on the second day)
l = 60 (since that will be the total number of spelling words given on the 21st day)
So, plugging in these values, we get:
S = 19/2 * (9 + 60) = 19/2 * 69 = 655.5
Therefore, by the end of the 21st day of school, Ms. Dubacek will have given her students a total of 6 + 655.5 = 661.5 new spelling words (rounded to the nearest whole number, this is 662).