I need help............ I don't know how to convert f(n)=f(n-1)+d into the sequence notation a(subscript) n=a+d(n-1)

- JozelynW

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- JozelynW

@dan815

- jim_thompson5910

is that all it says? or is there more that's given?

- JozelynW

No it says "Use your scenario to write the function for the 7th term in your sequence using sequence notation".

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## More answers

- JozelynW

this is what i filled in
Part 1: Create a scenario for an arithmetic sequence. For example, Jasmine practices the piano for 20 minutes on Monday. Every day she increases her practice time by 4 . 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.

- JozelynW

20 mins , increases , time by 4 that's what i added

- jim_thompson5910

so they want you to make up a sequence of your own? or can we use this example?

- JozelynW

they wanted me to make up my own based upon what i filled in and the formula above with the a

- jim_thompson5910

ok what sequence did you make up on your own?

- JozelynW

a(subscript) n=a+d(n-1)

- JozelynW

that is what help on filling in on this equation. In the f(n) version it made up one which is f(7)=f(6-1)+4

- JozelynW

when i fill in the sequence equation it looks like this a(subscript)7=a+4(7-1)

- jim_thompson5910

it says `Jasmine practices the piano for 20 minutes on Monday`
so the first term of this sequence is 20
making a = 20

- jim_thompson5910

the next day, tuesday, would be
a+d = 20+4 = 24 min
-------------------------
wednesday would be
24+4 = 28
etc etc

- JozelynW

so how would that be written

- jim_thompson5910

a = 20 and d = 4
they are plugged into `a+d(n-1)` to get the general nth term

- jim_thompson5910

so,
a+d(n-1) = 20+4(n-1) = ???

- JozelynW

thank you for you help.

- jim_thompson5910

glad to be of help

- JozelynW

@jim_thompson5910 need you help again with another 1

- jim_thompson5910

go ahead

- JozelynW

Use your scenario to write the formula for the 5th term in your sequence using sequence notation.

- JozelynW

the equation for geometric sequence is an=a1•rn−1.

- JozelynW

my info is
Anthony goes to the gym for 45 minutes on Monday. Every day he increases his gym time by 5 minutes.

- jim_thompson5910

`Anthony goes to the gym for 45 minutes on Monday. Every day he increases his gym time by 5 minutes.`
this is an ARITHMETIC sequence since the amount is increasing by a fixed amount.
d = 5 is the amount going up each time

- jim_thompson5910

if you said maybe something like "increases by 5%", then it would work

- JozelynW

i see what you're saying , I knew something wasn't right. So change it to 5%

- JozelynW

then what would i do

- jim_thompson5910

the first term is a = 45
the common ratio is r = 0.05 (decimal form of 5%)

- jim_thompson5910

no sorry, the common ratio would be 1.05
1+0.05 = 1.05

- JozelynW

so it would be a5=45 x1.05(7-1)

- jim_thompson5910

first term: 45
second term = (first term)*(common ratio)
second term = (45)*(1.05)
second term = 47.25
etc etc

- JozelynW

change the 5% to 1.05%?

- jim_thompson5910

I added on 1 because increasing by 5% is the same as multiplying by 1.05

- jim_thompson5910

the nth term should be
\[\Large a(r)^{n-1}\] then you plug in a = 45 and r = 1.05

- JozelynW

ok

- JozelynW

i have to use that exact equation above \[a _{4=45x 1.05(4}\]

- JozelynW

the x= times

- jim_thompson5910

the exponent should be n-1 = 4-1
so
\[\LARGE a_4 = 45*(1.05)^{4-1}\]

- JozelynW

well no, because i want to find the 5th term. I simplified it so I didn't put the -1 i just did it.

- JozelynW

so 5-1

- jim_thompson5910

oh, then you want to compute \(\LARGE a_5\) and not \(\LARGE a_4\)

- JozelynW

yes it's a5 not a4

- JozelynW

they wanted me to find a5 the fifth term.

- jim_thompson5910

I see

- JozelynW

ok so the answer would be what i said rightttt

- jim_thompson5910

yes, it would be \[\LARGE a_5 = 45*(1.05)^{4}\]

- JozelynW

Thank you, I may need help in like 3 mins again 1 more

- jim_thompson5910

ok

- JozelynW

a_(5=45 ×〖1.05〗^(5-1) ) @jim_thompson5910

- JozelynW

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.

- jim_thompson5910

I think you meant to write
\[\LARGE a_5 = 45 \times 1.05^{5-1}\] right?

- JozelynW

Yes, but i don't know how to make it look like that, how do you do that?

- JozelynW

the geometric series formula Sn=
a1−a1rn
1−r

- jim_thompson5910

you can use the equation editor (click the equation button below the text box)
I typed in `\LARGE a_5 = 45 \times 1.05^{5-1}` surrounded by `\[` and `\]`

- jim_thompson5910

as for the summation formula, it would be
\[\Large S_n = a*\frac{1-r^n}{1-r}\]

- jim_thompson5910

which is equivalent to the form you wrote

- JozelynW

where the a is by itself it should be with the 1 at the top

- jim_thompson5910

yes the two are equivalent
\[\Large S_n = a*\frac{1-r^n}{1-r} = \frac{a-a*r^n}{1-r}\]

- JozelynW

I'm going to screenshot it

- JozelynW

##### 1 Attachment

- jim_thompson5910

yeah which is what I wrote here
\[\Large S_n = \frac{a-a*r^n}{1-r}\]

- jim_thompson5910

there are 2 versions of the same thing really

- JozelynW

ok

- JozelynW

##### 1 Attachment

- jim_thompson5910

they want you to add up a bunch of terms and use the Sn formula to do it quickly

- jim_thompson5910

so for instance, add up the first 8 terms and compute S8

- JozelynW

So I"m using what you are saying as a example, because Idon't want to seem as a cheater

- jim_thompson5910

you can use another value of n

- JozelynW

ok 5

- JozelynW

Oh it says use the same scenario

- JozelynW

from part 2

- jim_thompson5910

so a = 45 and r = 1.05

- JozelynW

right ,but i need to make a question now

- JozelynW

Maybe I can say Anthony goes to the gym at 10 am for 45mins, then
IDK what im doing

- jim_thompson5910

so you have to make a completely different scenario?

- JozelynW

no just use the scenario from part 2 to make up a question

- JozelynW

i just seen an example on my math lesson so here is something similar "find the sum of the first 5 terms of the geometric series

- JozelynW

but I don't know what numbers are suppose to be in the geometric series
here is the example

##### 1 Attachment

- jim_thompson5910

ok so you'll plug a = 45 and r = 1.05 into that Sn formula
then you pick any n value you want (you picked n = 5 I think) and plug that in as well

- jim_thompson5910

\[\Large S_n = \frac{a-a*r^n}{1-r}\]
\[\Large S_5 = \frac{45-45*1.05^5}{1-1.05}\]
\[\Large S_5 = ???\]

- JozelynW

is it like the example?

- jim_thompson5910

yes

- JozelynW

ok than so what would be the geometric series than for the question?

- jim_thompson5910

I'm not sure what you're asking exactly?

- JozelynW

because i need to write a question; in the example question in the lesson it has something in the question that says geometric series look at the screenshot again

- JozelynW

I think it means 3 numbers that have a common ratio of 5%

- jim_thompson5910

you mean they want you to add up the first three terms of the geometric sequence?

- JozelynW

idk honestly. I'm just listening to you

- JozelynW

does it look like what it mean in the picture

- JozelynW

this is a project and it doesn't really explain much

- jim_thompson5910

yeah I wish it had clearer instructions. I think they want you to add up a bunch of terms
so say you wanted to add up the first 7 terms
a = 45
r = 1.05
n = 7
\[\Large S_n = \frac{a-a*r^n}{1-r}\]
\[\Large S_7 = \frac{45-45*1.05^7}{1-1.05}\]
\[\Large S_7 = \frac{45-45*1.4071004}{1-1.05}\]
\[\Large S_7 = \frac{45-63.319518}{1-1.05}\]
\[\Large S_7 = \frac{-18.319518}{-0.05}\]
\[\Large S_7 = 366.39036\]
The approximate sum of the first 7 terms is 366.39036

- JozelynW

So the question would be "Find the sum of the first 7 terms

- jim_thompson5910

yes the work shown above would apply to that question

- JozelynW

Thank you, your name should say lifesaver. You just helped me finish out my math class.

- jim_thompson5910

I'm glad I could be of help

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