Question

to save money for holiday presents, a person deposits $5 in a savings account on january 1, and then deposits an additional $5 every week thereafter until christmas.
a. write a sequence for the money in that savings account for the first 10 weeks of the year.
□,□,□,□,□,□,□,□,□,□
b. write the general term of the sequence in part a. $a_n =$□
c. if there are 50 weeks from january 1 to chrismas, how much money will be available for spending on christmas presents?
there will be $□ available for spending on christmas presents.
question help: ebook

Explanation:

Step1: Define initial deposit and weekly addition

Initial deposit (week 1): $5; weekly addition: $5. So each week’s amount = 5 × week number.

Step2: Generate first 10 terms

Week 1: 5×1=5; Week2:5×2=10; ... Week10:5×10=50.

Step3: Find general term

General term \(a_n = 5n\) (n=week number).

Step4: Calculate for 50 weeks

Substitute n=50 into \(a_n\): \(5×50=250\).

Answer:

a. 5, 10, 15, 20, 25, 30, 35, 40, 45, 50
b. \(5n\)
c. 250