Question

Create a scenario for a geometric sequence. For example, Anthony goes to the gym for __20____ minutes on Monday. Every day he ___increases______his gym time by ____10________. 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.

Monday - 20 minutes
Tuesday - 30 minutes
Wednesday - 40 minutes
Thursday - 50 minutes
Friday - 60 minutes

Answer 1

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

I already have my data, I just need help to write a formula for my 5th term , using sequence notation and then i need help with part 3.

Answer 3

Give us your data.

Answer 4

Anthony goes to the gym for __20____ minutes on Monday. Every day he ___increases______his gym time by ____10________. 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.

Monday - 20 minutes
Tuesday - 30 minutes
Wednesday - 40 minutes
Thursday - 50 minutes
Friday - 60 minutes

Answer 5

That is an arithmetic sequence. Not a geometric sequnce.

Answer 6

@ranga same here.

Answer 7

You can say he goes to the gym for 20 minutes on Monday and everyday he increases his gym time by 10%. Then calculate the time for Tue, Wed, etc.

Answer 8

and i would keep multiyplying by 10 for each day ?

Answer 9

Not by 10. It is an increase of 10% (PERCENT). So you multiply by 1.1 each time (multiplying by 1.1 reflects an increase by 10%).

Answer 10

10% is 0.1

Answer 11

so i do 20 times what?

Answer 12

20 * 1.1 = 22 minutes

Answer 13

Then 22 * 1.1 = 24.2
....

Answer 14

oh ok, so what about part 3?

Answer 15

Complete Thursday and Friday too.

Answer 16

yeah i already wrote it
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 17

by the way the 'n' in 'Sn' is an exponent but at the bottom of S

Answer 18

"series" implies summing up or adding up.
So if were were to ask the question how much time did Anthony spend at the gym from Monday to Friday then we will have to add the time from Monday to Friday..

Answer 19

ok... but whats Sn

Answer 20

whats the formula template im suppose to use to plug in whatever im suppose to plug in

Answer 21

There is a standard formula for the sum of the first n terms of a geometric series:\[\Large S _{n} = a \frac{ 1 - r^n }{ 1-r }\]

Answer 22

where a is the first term and r is the common ratio.
Here a = 20 minutes and r = 1.1 and to find out the total time at the gym from Mon-Fri, n = 5 days. Plug the numbers into the formula and tell me what u get.

Answer 23

wait so the total time from mon-fri is all the minutes added right ?

Answer 24

Yes. But they are asking you to use the formula to find the sum. Do that first and later also manually add up the times for the 5 days and see if they match.

Answer 25

S(5)=20 1-1.1^5 / 1-1.1

Answer 26

yes. use calculator to find sum. make use of parenthesis properly.

Answer 27

no. 20 * ( 1 - 1.1^5 ) / ( 1 - 1.1) = ?

Answer 28

123 is not correct. Use parenthesis.

Answer 29

122 ?

Answer 30

No. Make use of the parenthesis in your calculator and type them just as I wrote them above: 20 * ( 1 - 1.1^5 ) / ( 1 - 1.1) =

Answer 31

i did

Answer 32

i got 122.102, u try it

Answer 33

@ranga

Answer 34

Yes. 122.102.
Now list the gym time for the 5 days we did earlier. We did 3 days:
20, 22, 24.2 and we need data for Thu & Fri. List them here and using calculator add the 5 numbers to see if the total agrees with the total calculated using formula.

Answer 35

Monday - 20 minutes
Tuesday - 22 minutes
Wednesday - 24 minutes
Thursday - 27 minutes
Friday - 30 minutes
= 123

Answer 36

No. Mon - 20. Tue - 20 * 1.1 = 22, Wed - 22 * 1.1 = 24.2
Thu - 24.2 * 1.1 =

Answer 37

27

Answer 38

Come on. You just have to use your calculator to multiply two numbers.

Answer 39

Thu - 26.62 minutes
Fri - 26.62 * 1.1 = ?

Answer 40

29.282

Answer 41

rounded to 30

Answer 42

You can do the rounding off normally but here the sequence has to be geometric. That means the ratio must be the same when you divide successive numbers. if you round off the ratio will not be the same.

Answer 43

ok wat now

Answer 44

@tkhunny

Answer 45

These are the 5 numbers that you should list for part 2:
Mon - 20 minutes
Tue - 22 minutes
Wed - 24.2 minutes
Thu - 26.62 minutes
Fri - 29.282 minutes

And for your own verification, you can add these 5 numbers and see if it matches the total calculated using the formula earlier.

Answer 46

It is only a coincidence that we both picked 10% increases. There is nothing magic about that. You could use 20% increases and multiply by 1.2 each time.

Answer 47

@ranga ... it does

Answer 48

@ranga so now what ... they;re both the same so...

Answer 49

so you can be sure your calculations are correct. So all three parts have been answered.

Answer 50

ok so this is what im submitting

Task 3

Create a scenario for an arithmetic sequence. For example, Jasmine practices the piano for _10_____ minutes on Monday. Every day she ____increases_______ her practice time by __15 minutes_______. 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.
Monday- 10 minutes
Tuesday - 25 minutes
Wednesday - 40 minutes
Thursday - 55 minutes
Friday - 70 minutes
Saturday - 85 minutes
Sunday - 100 minutes
She will practice piano for 100 minutes on the 7th day, Sunday.

function : An = a1 + d(n – 1)
Day N = 10 +15(n-1)
Day 7= 10+15 (7-1)

part 2

Create a scenario for a geometric sequence. For example, Anthony goes to the gym for __20____ minutes on Monday. Every day he ___increases______his gym time by ____10%________. 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.
(i rounded the decimals here)
Mon - 20 minutes
Tue - 22 minutes
Wed - 24.2 minutes
Thu - 26.62 minutes
Fri - 29.282 minutes
He will spend 29.282 minutes at the gym on the 5th day, Friday.

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.

Sn=a*1−r^n/1−r
where a is the first term and r is the common ratio.
Here a = 20 minutes and r = 1.1 and to find out the total time at the gym from Mon-Fri, n = 5 days.

S(5)=20 1-1.1^5 / 1-1.1
=122.102