Question

The number of spelling words Lucas still has to memorize n days after he began studying for a spelling bee is defined by the arithmetic sequence f(n) = 200 - 12(n - 1). How many words does Lucas still have to memorize n days after he began studying for the spelling bee?

Answer 1

Lucas has to memorize 200 words for a spelling bee, with the number decreasing by 12 words each day described by the arithmetic sequence f(n) = 200 - 12(n - 1).

Step-by-step explanation:

The number of spelling words Lucas still has to memorize n days after he began studying for a spelling bee is represented by an arithmetic sequence given by the function f(n) = 200 - 12(n - 1). To find out how many words Lucas has left to memorize on any given day n, we plug the day number into the sequence. For example, on the first day (n = 1), the calculation would be f(1) = 200 - 12(1 - 1) = 200, meaning Lucas starts with 200 words to memorize. On the second day (n = 2), Lucas would have f(2) = 200 - 12(2 - 1) = 200 - 12 = 188 words left to memorize. This pattern continues, decreasing the words to memorize by 12 each subsequent day.