Posts Tagged ‘sequences and series’

Spotted on my Facebook newsfeed: New Year’s resolution to save, based on this blog post, which shows a money challenge that results in an extra \$1378 at the end of the year.

The original blog post comments have become a flame war of sorts. Folks call \$1378 practically nothing and others pipe up to defend saving at all. There are arguments about luxuries versus necessities. Some say that putting money in bank accounts is stupid.

However, there are some comments that could spark a discussion related to arithmetic sequences and series and the feasibility of doing these savings challenges in real life:

1) “I’d think it would be easier to deposit \$25 per week = \$1300. I’d think the larger amounts would be more difficult for some people to cough up each week, and they’d give up. Now if they can add \$2 more per week, that would give them \$1404 in the end. Or give them several options just to show what they could end up with in different denominations, ie \$50 and \$100. \$2600 and \$5200….”
2) “yes, people living in poverty are not in a position to save for a ski holiday. the beauty of this idea is that
it makes it a bit more fun
in the first month or so, it helps form a painless (for most people) habit. the difficulty of putting in \$25 per week (and more) is balanced by the difficulty in letting yourself down by abandoning the dream/ project. personally, I’d find putting \$25 in a jar hard to start, but I’d also find giving up on my habit of the past 6 months hard.”
3) “We have done this the last few years but do it backwards, for us it was much more feasible to save the bigger amounts earlier in the year compared to during the holiday season.”
4) “So do it in different increments instead. You could do \$0.25 or \$0.50 increments. You won’t save as fast, but it’s better than nothing.”
5) Someone even suggested a geometric sequence: ““DOUBLE IT”
Starts off in cents so you may be able to do it day after day at first however when as the game gets further just do it when you budget and save to finish your game goal. Challenge yourself make it a great goal of money.
Day 1. -One little penny. “Double it” Day 2- two pennies
Day 3 – only four lousy pennies (it’s small now oh but wait there’ more.
Day 5 – 8 pennies (Don’t cheat now and put all of it in for the week this is where the game comes into play and you start building your discipline for when it starts getting difficult. It makes it so you want to participate all the way through starting with only a penny. you will want to be putting money aside for the days to come because it starts growing fast after we are on day 11.
Day 6 – 16 cents. Day lucky 7 – 32 cents
Day 8 – 64 cents Day 9 – \$1.28
Day 10 – \$2.56. Day 11 – \$5.12
Day 12 or day of 12th deposit – \$ 10.24 and so on”

I asked one section of students to create and solve their own geometric series word problem. After my repeated tirades about seeing mice in the classroom over the past two weeks, one provided this:

“There has been a mouse infestation inside JQUS. The first day there was 4 mice seen. On the second day there were 12 mice, third day 36 mice. How many mice will there be on the 26th day?”