Question

Help Me Plz Important Algebra Question!

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

@mtbender74 plz help...

Answer 3

so what is an arithmetic sequence and what is a geometric sequence?

Answer 4

An arithmetic sequence is a sequence with a common difference and a gometric sequence is a sequence with a common ratio

Answer 5

exactly...in other words, arithmetic sequences add/subtract the same amount and geometric sequences multiply/divide the same amount

Arithmetic: 2, 4, 6, 8, 10, ...
Geometric: 2, 4, 8, 16, 32, ...

Answer 6

ok lol

Answer 7

So for each of part 1 and 2, you need to pick an initial amount of time, then pick if it will be increasing or decreasing, and then pick the amount of increase/decrease

Answer 8

20 minuits, increases (make her work harder lol), 10% to make it easy

Answer 9

10% is a geometric...

Answer 10

oh ok sorry

Answer 11

10 minuites

Answer 12

so, how long will she practice on the 7th day?

Answer 13

the nth term of an arithmetic sequence is found by \[a_{n}=a_{1}+r(n-1)\]

Answer 14

1 1/2 hours

Answer 15

check that again...you don't add the 10 minutes the first day, so how many 10 minutes increases are there by the 7th day?

Answer 16

80 mins

Answer 17

better :)

Answer 18

Now for part 2, it's the same sort, but you increase by a factor (10%, twice, 10 times, etc.)

Answer 19

That was part 1 already?!

Answer 20

as long as you can take the equation above and fill in the piece for last piece of part 1 :)

Answer 21

ok so for part 2 lets put in the same things but 10%

Answer 22

ok...so 20 minutes, increase by 10% each time

Answer 23

yup!

Answer 24

now you want the 5th day...

the general form of a geometric is\[a_{n}=a_{1}r^{n-1}\]

but here we have to be careful because since we are *increasing* each day is 110% of the previous...so r=1.1

Answer 25

so \[a_{5}=?\]

Answer 26

?
isn't it 0.1x

Answer 27

well, let's think about it...we increase 10%, so the second day would be 20 + 20(0.1) = 20(1 + 0.1) = 20(1.1)

Answer 28

uhh still confused

Answer 29

ok...let's talk about geometrics for a bit.

let say we want to start at 3 and double each time...ok?

Answer 30

2x

Answer 31

oh i think i got it

Answer 32

\[a_{1}=3\]
\[a_{2}=2a_{1}=3(2)\]
\[a_{3}=2a_{2}=[3(2)](2)=3(2)^{2}\]

so we see the general formula forming
\[a_{n}=a_{1}r^{n-1}\]

Answer 33

but since you have a percentage increase, we have to add 100% since tomorrow we will do 110% of today

Answer 34

so in that case, r=1.1

if we did a 10% decrease, r=.9

Answer 35

Oh ok

Answer 36

makes more sense?

Answer 37

yea

Answer 38

so you think you have your general formula for 20 minutes with a 10% increase?

Answer 39

until when

Answer 40

well, the general formula for the nth term would be \[a_{n}=20(1.1)^{n-1}\]

but you want the 5th term...

Answer 41

28

Answer 42

\[a_{5}=20(1.1)^{4}=?\]

Answer 43

what does a stand for

Answer 44

\[a_{n}\]
means the nth term of the sequence....

Answer 45

29.282 {admitting he finally used a claculator

Answer 46

lol...there's nothing wrong with that...i certainly wouldn't do (1.1)^5 by hand

Answer 47

y not

Answer 48

it would get a little boring by the third or fourth multiplication...

Answer 49

lol

Answer 50

Now, for part 3, we need to find a general formula for \[S_{n}\]
which is the sum of the first n terms of the sequence

This would be like me asking, "How much total gym time would Anthony have spent after the 5th day?"

Answer 51

well, we can calculate all five days and add them up, but if we then changed it to a month, you'd really not like doing it by hand...

so let's see if we can get an equation for it directly...

\[\sum_{k=0}^{n-1}(ar^{k})=a(\frac{1-r^{n}}{1-r})\]
is the formula you would use where a is your initial amount, and r is the same as before

Answer 52

so \[S_{n}=a(\frac{1-r^{n}}{1-r})\]
where a=20, r=1.1

Answer 53

fill those in and Part 3 should be done

Answer 54

I apologize my internet was down even when it showed i was online it always happens i have 2 megabits per second

Answer 55

weird...
to sum up, part 3 consists of a question similar to the one above, and then is answered using the formula for Sn a couple posts ago :)

Answer 56

So what do i put for part 3?

Answer 57

you see the sample question about 6 posts ago?

it starts with something like that
then, you need to answer the question using the formula above
\[S_{n}=a(\frac{1-r^{n}}{1-r})\]

Answer 58

So start with a similar question...

Answer 59

oh boy too many formulas

Answer 60

lol...i know...

Answer 61

Mark goes to the park for ______ minutes on Sunday. Every day he _________his park time by ____________. If he continues this pattern, how many minutes will he spend at the park on the 5th day?

Answer 62

Not quite the question we were looking for...

"Now, for part 3, we need to find a general formula for
Sn

which is the sum of the first n terms of the sequence

This would be like me asking, "How much total gym time would Anthony have spent after the 5th day?"
"

Answer 63

That's the post i was referring to :)

Answer 64

oh sry lol

Answer 65

so that's the sort of question you need...

then you would use the same a and r from Part 2 with however many days you want to sum up in the formula above, and that is Part 3 :)

Answer 66

what formula which one

Answer 67

@mtbender74