Question

PLEASE HELP I WILL FAN AND MEDAL!!

Answer 1

Part 1: Create a scenario for an arithmetic sequence. For example, Jasmine practices the piano for ______ minutes on Monday. Every day she ___________ her practice time by _________. If she continues this pattern, how many minutes will she practice on the 7th day? Be sure to fill in the blanks with the words that will create an arithmetic sequence. Use your scenario to write the function for the 7th term in your sequence using sequence notation.
Part 2: Create a scenario for a geometric sequence. For example, Anthony goes to the gym for ______ minutes on Monday. Every day he _________ his gym time by ____________. If he continues this pattern, how many minutes will he spend at the gym on the 5th day? Be sure to fill in the blanks with the words that will create a geometric sequence. Use your scenario to write the formula for the 5th term in your sequence using sequence notation.
Part 3: Use your scenario from part 2 to write a question that will lead to using the geometric series formula. Use the formula to solve for Sn in your scenario.

Answer 2

@pooja195 @math&ing001

Answer 3

Ok so they want you to create an arithmetic sequance meaning something that increases each day in this senario. For example you can say she trains 1h30 on monday then she increases her sessions with 4 minutes every day.

Answer 4

Okay, so how do I make the function?

Answer 5

Let's say we use my example. So initial practice time is 1h30=90min and she increases her practice time by 4min each day, so each day she adds 4min to the training time of the day before. That would mean for the 7th day \[a _{7}=a _{6}+4\]

Answer 6

\(a _{n}\) is the training time for day n.

Answer 7

So would she would have 114 minutes on the seventh day?

Answer 8

Yep !

Answer 9

Yeah sure, what example did you use for part 2 ?

Answer 10

I haven't done that yet but I understand it now :)

Answer 11

Well it's not really the same as the first. This is now a geometric sequence, so you'll need to multiply.

Answer 12

Alright, so can you help me with that too? Sorry, I get confused with word problems really easily

Answer 13

This time you choose an initial training time and a common ratio, by which you multiply each day the training time of the day before.

Answer 14

Actually the common ratio is not in minutes, it's just a number. For example, I train 10min the first day, then I multiply my training time by 2 each day. So on the second day I'll train 20min, on the third 40min, on the fourth 80min...

Answer 15

Oh okay :) So on the 5th day he would have trained 160 minutes?

Answer 16

In this example, yeah

Answer 17

So how would this be written in sequence notation?

Answer 18

a5=2*a4

Answer 19

Although, I would really want you to make your own examples so you can truly understand.

Answer 20

Oh, I'm just asking if you can do it with your example so I would learn how to do it. I'm making my own examples, don't worry. :)

Answer 21

So can you help me with part 3 now?

Answer 22

Awesome !

Answer 23

Yeah, sure! In the third part they want you to use geometric series formula using the example from part 2.
One easy question from part 2 would be : how much time did he train in total (from day1 to day5) ?

Answer 24

Okay, so what would the formula for that question be?

Answer 25

The formula to use is the geometric series formula, which I'm sure you already seen.

Answer 26

Okay..

Answer 27

Thanks @math&ing001

Answer 28

Welcome !