Question

Greta must volunteer 225 hours for a community service project. She plans to volunteer for 6 hours

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.