Question

Greta must volunteer 225 hours for a community service project. She plans to volunteer for 6 hours
each week. The sequence shown represents the number of volunteer hours she has left after three
weeks have passed.
225, 219, 213, 207, ...
a.
A. Describe this sequence.

B. Use a formula to determine how many volunteer hours Greta has left to fulfill her requirement after 33 weeks have passed. Show your work.

C. Which formula should you use to determine how many volunteer hours Greta has left to fulfill her requirement after 40 weeks have passed? Explain your reasoning.

D. Calculate the number of volunteer hours Greta has left to fulfill her requirement after 40 weeks have passed. Explain what your answer means in terms of the problem situation.​

Answer 1

Answer:

A. "an arithmetic sequence with a common difference (d) of -6."

B. 33 hours

C. $a_n=a_1+(n-1)d$

D. See below

Step-by-step explanation:

A.

Since the sequence lessens by 6, this is an arithmetic sequence with a common difference (d) of -6.

B.

The formula for term of arithmetic sequence is:

$a_n=a_1+d(n-1)$

Wher a_1 is the first term and d is the common difference. Since we want to find after 33 weeks, we plug in 33 into n:

$a_{33}=225 + (-6)(33-1)\\a_{33}=33$

She will have left 33 hours

C.

We will use the arithmetic sequence term formula written above, that is:

$a_n=a_1+(n-1)d$

THis gives us the amount of hours left after a certain number of weeks.

D.

We plug in 40 into n and find the hours left:

$a_{40}=225+(40-1)(-6)\\a_{40}=225-234\\a_{40}=-9$

THis term is NEGATIVE, which means that Greta will not have to work 40 weeks to fulfill the target of 225 hours. She needs to work less.