More sequences

Question

To save money for holiday presents, a person deposits $15 in a savings account on January 1, and then deposits an additional $15 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

C If there are 50 weeks from January 1 to Chrismas, how much money will be available for spending on Christmas presents?  

Answer 1

A.  Start with 15 (drop dollar sign for convenience). After 1 week 15 + 15 = 30 so first term, corresponding to week 1 is 30. After two weeks, add another 15: 30 + 15 = 45; after 10 weeks: 15 + 10x15 = 15 + 150 = 165. The sequence written out for 10 weeks is: 30, 45, 60, 75, 90, 105, 120, 135, 150, 165.

 

B.  After n weeks the amount in the account will be: 15 + 15n = 15(n + 1).

 

C.  Assuming the last deposit and the shopping is done on Christmas day! If so, then use the formula from B with n = 50:

  

15(50 + 1) = 765. But maybe this is a trickier question and you are supposed to realize that the shopping for Christmas would have to be done before Christmas and that the deposits are made "until" Christmas. In that case, deposits of $15 are made for only 49 of the 50 weeks, so 49 is the number to use in the formula in part B:  15(49 + 1) = 750. So it depends how you are supposed to interpret the information in the question and it's a bit unclear. Do it both ways to be on the safe side!