Noreen recently took a job helping people register to vote. The job has a mandatory 10-day period of probation during which her success rate is strictly monitored. On her first day, she registered 30 people. Then, for each of the next 9 days, she registered 4 more people than she did on the previous day. How many people did she register altogether during her probationary period?

F. 300
G. 340
H. 480
J. 560
K. 600

arithmetic series

see
http://www.mathwords.com/a/arithmetic_series.htm
here a1 = 30 and d = 4 and n = 10

I still don't get it.

To find out how many people Noreen registered altogether during her probationary period, we need to calculate the total number of people she registered each day and sum them up.

First, we know that on her first day, she registered 30 people.

Then, for each of the next 9 days, she registered 4 more people than the previous day. This means that on the second day, she registered 30 + 4 = 34 people. On the third day, she registered 34 + 4 = 38 people. And so on.

To calculate the total number of people she registered during her probationary period, we add up the number of people she registered each day.

30 + 34 + 38 + ... (continue this pattern for 9 days)

To make this calculation easier, we can use the formula for the sum of an arithmetic sequence:

Sn = (n/2)(a + l),

where Sn is the sum of the sequence, n is the number of terms, a is the first term, and l is the last term.

In this case, the number of terms is 9 (9 days of probation), the first term is 30, and the last term is 30 + 4*(9-1) = 30 + 4*8 = 30 + 32 = 62.

Using the formula, we can calculate the sum:

Sn = (9/2)(30 + 62)
= 4.5 * 92
= 414

So, Noreen registered a total of 414 people during her probationary period.

None of the answer choices provided matches 414. However, we can see that the answer choices given include 300, 340, 480, 560, and 600. Among these choices, the closest number to 414 is 480.

Therefore, the closest answer choice is H. 480.