Question

Pretty Easy Question i have most of it done

Answer 1

Part 1: 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 5 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.

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.

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 \[S_{n}\] in your scenario.

Answer 2

i already created the scenarios i jus needa put the stuff in sequence notation and find the 7th term

Answer 3

easier than it looks

Answer 4

@dan815 help?

Answer 5

whats sequence notation?

Answer 6

okay tell me your sceneario

Answer 7

Thats the one it came with blanks and i filled them in

Answer 8

i filled in the numbers

Answer 9

Sequence notation is like
1+2+3+4..... = \[\sum n \]

Answer 10

o.o

Answer 11

oh okay then lets see what kinda arith seq we are dealing with

Answer 12

i think its 80 minuites but i dont know how to present it

Answer 13

so we sharted with 10
2nd day = 10+5
3rd day = 10+5+5
4th day = 10 + 5+5+5
...
The sequence is going like
10+15+20+25....
Sn=10+5n, if u want n at 1st day being tuesday and 0th day being monday

Answer 14

so Sn=x+n is the sequence notation?

Answer 15

The proper notation
\[S_n=10+5(n-1)\]
\[S_7=10+5(7-1)\\
S_7=10+30=40
\]

Answer 16

me confused...

Answer 17

what does the formula look like?

Answer 18

lik this
\[S_n=10+5(n-1)\]
You can also simplify this to be
\[S_n=5+5n\]

Answer 19

where is the nth day we care about

Answer 20

\[a _{n} = a + (n-1)d\] where d is your comman difference, and a is first term.

Answer 21

hmm how I explain this.. you know about lines or functions.. like
x y
1 10
2 15
3 20
4 25
... ....
This is a linear equation as y is increasing by 5 everytime so a constant slope..
Find the slope and y intercept write this equation in
y=mx+b form
where x = the number of day we want
and Y = practice time

Answer 22

put n = 7 in above equation you will get your result.

Answer 23

What is (n-1)?

Answer 24

its the formula for general term of an A.P

Answer 25

hold on miracrown will teach you... she is a good explainer

Answer 26

@Miracrown

Answer 27

lol

Answer 28

let an A.P. be

\[a _{1}, a _{2}, a _{3}, ...........................a _{n-1}, a _{n}\]

Answer 29

im not getting what ur saying @cp9454

Answer 30

@dan815 ur busy?

Answer 31

\[a _{1}= a\]
\[a _{2}= a+d\]
\[a _{3}= a+2d\]
.
.
.
.\[a _{n} = a+(n-1)d\]

Answer 32

here \[a_{n} is the nth term.\]

Answer 33

???

Answer 34

\[a _{n}\] is the nth term.

you just need to put the values of first term, comman difference, and the term you want to find. for example you want to find the 7th term,
your formula should be,
\[a _{7}= a+(7-1)d\]

Answer 35

what do the variables stand for?

Answer 36

a is first term,
d is comman difference, e.g. it is 5 in your case
n is no. of terms.

Answer 37

still not getting @camerondoherty

Answer 38

listen, its a formula just use it and you will see, how it works. and you will easily be able to solve the problems. @camerondoherty

Answer 39

i got it but what about the second one wouldnt the equation or formula be different?

Answer 40

no its the univrsal formula it is apllicable to all the APs in the world.

Answer 41

because its a geometric sequence

Answer 42

Yes okay for 2nd one
you have a 10% increase so multiplied by 1.1 everytime

Answer 43

oh ok

Answer 44

so hold on let me make the equation for it

Answer 45

GP has different formula

Answer 46

\[S_{5}=20+1.1(5−1)\]

Answer 47

\[G_n=20*(1.1)^{n-1}\], for n>=1

Answer 48

close

Answer 49

o

Answer 50

So \[G _{5}=20\times(1.1)^1\]

Answer 51

we need multiplyig by 1.1 so
day 1= 20
day 2 =20*1.1
day3= 20*1.1*1.1-=20*1.1^2
day4=20*1.1^3
day5=20*1.1^4
Dayn=20*1.1^(n-1)

Answer 52

to the power of 4

Answer 53

oh whoops xD i was thinking of one but i knew it was 4

Answer 54

ok good :)

Answer 55

So the equation is this? http://prntscr.com/416i9z

Answer 56

Ill take that as a yes...

Answer 57

yes

Answer 58

Is this good? http://prntscr.com/416jt6

Answer 59

@dan815 ?

Answer 60

and can someone explain to me how to do the last one?

Answer 61

Now its the sum of a geometric serives

Answer 62

Sum of what geometic serives?

Answer 63

yeah so
\[S_n=G_1 + G_2 + G_3...+G_n\]
They want yo to find a formula for this now we know what G_n can be written as, lets say instead of 20, it was P, and instead of 1.1 it was r for rate

\[S_n=P*r^1+P*r^2+...p*r^n\]

Answer 64

oops it should actually go lke this dont forget that n-1

Answer 65

\[S_n=P+P*r^1+P*r^2+...p*r^{n-1}\]

Answer 66

say what? Im confused...

Answer 67

note the first term is P only since r^0 =1

Answer 68

too many Ps' and Gs'

Answer 69

xD

Answer 70

Wait so they want me to write that?

Answer 71

okay wait, just a scenario for part 3 first, i dont think they want you to derive the formnula really... they maybe just expect you to know the formula

Answer 72

write a scenario*

Answer 73

like the whole question thingy?

Answer 74

if so: 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 75

well ya it can be something simple tho like /how long has anthony worked out after 10 days in total

Answer 76

yeah expect the last question would be like how many mins will be spend at the park if you combine all 5 days

Answer 77

Mark goes to the park for 40 minutes on Sunday. Every day he increases his park time by 20%. If he continues this pattern, how many minutes will he spend at the park on the 5th day?

Answer 78

will he*

Answer 79

Mark goes to the park for 40 minutes on Sunday. Every day he increases his park time by 20%. If he continues this pattern, how many minutes will he spent at the park on the first 5 days altogether?

Answer 80

i said tht -_-

Answer 81

altogether! u dummy

Answer 82

\[S _{5}=40(2.2)^{5-1}\]

Answer 83

lol

Answer 84

no Cammy this one different its a sum of all the days from 1 to 5

Answer 85

i dont get it...

Answer 86

we want ot know how much time he has spent at the part in total

Answer 87

from day 1 to 5?

Answer 88

yes

Answer 89

altogether? all added up?

Answer 90

yes, thats what that S means S is for a sum

Answer 91

Like what if I asked you to fine how much total time he spent at the park in like 7 days all combined...
G_7 is only telling u his time for the 7th day not all the previous days together

Answer 92

\(S _{5}=40(2.2)^{5-1}\)
\(S _{4}=40(2.2)^{4-1}\)
\(S _{3}=40(2.2)^{3-1}\)
\(S _{2}=40(2.2)^{2-1}\)
\(S _{1}=40(2.2)^{1-1}\)

Answer 93

noo lol that is G_1 , G_2 G_3.. G_5

Answer 94

S is the sum of it
\[S_5=G_1+G_2+G_3+G_4+G_5\]

Answer 95

lol whoops just change the S to G

Answer 96

okok soo now use that Sn formula if u have it already

Answer 97

wait so theres another formula?!