JozelynW
  • JozelynW
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)
Mathematics
  • Stacey Warren - Expert brainly.com
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schrodinger
  • schrodinger
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
JozelynW
  • JozelynW
@dan815
jim_thompson5910
  • jim_thompson5910
is that all it says? or is there more that's given?
JozelynW
  • 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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JozelynW
  • 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
  • JozelynW
20 mins , increases , time by 4 that's what i added
jim_thompson5910
  • jim_thompson5910
so they want you to make up a sequence of your own? or can we use this example?
JozelynW
  • JozelynW
they wanted me to make up my own based upon what i filled in and the formula above with the a
jim_thompson5910
  • jim_thompson5910
ok what sequence did you make up on your own?
JozelynW
  • JozelynW
a(subscript) n=a+d(n-1)
JozelynW
  • 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
  • JozelynW
when i fill in the sequence equation it looks like this a(subscript)7=a+4(7-1)
jim_thompson5910
  • 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
  • jim_thompson5910
the next day, tuesday, would be a+d = 20+4 = 24 min ------------------------- wednesday would be 24+4 = 28 etc etc
JozelynW
  • JozelynW
so how would that be written
jim_thompson5910
  • jim_thompson5910
a = 20 and d = 4 they are plugged into `a+d(n-1)` to get the general nth term
jim_thompson5910
  • jim_thompson5910
so, a+d(n-1) = 20+4(n-1) = ???
JozelynW
  • JozelynW
thank you for you help.
jim_thompson5910
  • jim_thompson5910
glad to be of help
JozelynW
  • JozelynW
@jim_thompson5910 need you help again with another 1
jim_thompson5910
  • jim_thompson5910
go ahead
JozelynW
  • JozelynW
Use your scenario to write the formula for the 5th term in your sequence using sequence notation.
JozelynW
  • JozelynW
the equation for geometric sequence is an=a1•rn−1.
JozelynW
  • 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
  • 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
  • jim_thompson5910
if you said maybe something like "increases by 5%", then it would work
JozelynW
  • JozelynW
i see what you're saying , I knew something wasn't right. So change it to 5%
JozelynW
  • JozelynW
then what would i do
jim_thompson5910
  • jim_thompson5910
the first term is a = 45 the common ratio is r = 0.05 (decimal form of 5%)
jim_thompson5910
  • jim_thompson5910
no sorry, the common ratio would be 1.05 1+0.05 = 1.05
JozelynW
  • JozelynW
so it would be a5=45 x1.05(7-1)
jim_thompson5910
  • jim_thompson5910
first term: 45 second term = (first term)*(common ratio) second term = (45)*(1.05) second term = 47.25 etc etc
JozelynW
  • JozelynW
change the 5% to 1.05%?
jim_thompson5910
  • jim_thompson5910
I added on 1 because increasing by 5% is the same as multiplying by 1.05
jim_thompson5910
  • jim_thompson5910
the nth term should be \[\Large a(r)^{n-1}\] then you plug in a = 45 and r = 1.05
JozelynW
  • JozelynW
ok
JozelynW
  • JozelynW
i have to use that exact equation above \[a _{4=45x 1.05(4}\]
JozelynW
  • JozelynW
the x= times
jim_thompson5910
  • jim_thompson5910
the exponent should be n-1 = 4-1 so \[\LARGE a_4 = 45*(1.05)^{4-1}\]
JozelynW
  • 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
  • JozelynW
so 5-1
jim_thompson5910
  • jim_thompson5910
oh, then you want to compute \(\LARGE a_5\) and not \(\LARGE a_4\)
JozelynW
  • JozelynW
yes it's a5 not a4
JozelynW
  • JozelynW
they wanted me to find a5 the fifth term.
jim_thompson5910
  • jim_thompson5910
I see
JozelynW
  • JozelynW
ok so the answer would be what i said rightttt
jim_thompson5910
  • jim_thompson5910
yes, it would be \[\LARGE a_5 = 45*(1.05)^{4}\]
JozelynW
  • JozelynW
Thank you, I may need help in like 3 mins again 1 more
jim_thompson5910
  • jim_thompson5910
ok
JozelynW
  • JozelynW
a_(5=45 ×〖1.05〗^(5-1) ) @jim_thompson5910
JozelynW
  • 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
  • jim_thompson5910
I think you meant to write \[\LARGE a_5 = 45 \times 1.05^{5-1}\] right?
JozelynW
  • JozelynW
Yes, but i don't know how to make it look like that, how do you do that?
JozelynW
  • JozelynW
the geometric series formula Sn= a1−a1rn 1−r
jim_thompson5910
  • 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
  • jim_thompson5910
as for the summation formula, it would be \[\Large S_n = a*\frac{1-r^n}{1-r}\]
jim_thompson5910
  • jim_thompson5910
which is equivalent to the form you wrote
JozelynW
  • JozelynW
where the a is by itself it should be with the 1 at the top
jim_thompson5910
  • 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
  • JozelynW
I'm going to screenshot it
JozelynW
  • JozelynW
1 Attachment
jim_thompson5910
  • jim_thompson5910
yeah which is what I wrote here \[\Large S_n = \frac{a-a*r^n}{1-r}\]
jim_thompson5910
  • jim_thompson5910
there are 2 versions of the same thing really
JozelynW
  • JozelynW
ok
JozelynW
  • JozelynW
1 Attachment
jim_thompson5910
  • jim_thompson5910
they want you to add up a bunch of terms and use the Sn formula to do it quickly
jim_thompson5910
  • jim_thompson5910
so for instance, add up the first 8 terms and compute S8
JozelynW
  • JozelynW
So I"m using what you are saying as a example, because Idon't want to seem as a cheater
jim_thompson5910
  • jim_thompson5910
you can use another value of n
JozelynW
  • JozelynW
ok 5
JozelynW
  • JozelynW
Oh it says use the same scenario
JozelynW
  • JozelynW
from part 2
jim_thompson5910
  • jim_thompson5910
so a = 45 and r = 1.05
JozelynW
  • JozelynW
right ,but i need to make a question now
JozelynW
  • JozelynW
Maybe I can say Anthony goes to the gym at 10 am for 45mins, then IDK what im doing
jim_thompson5910
  • jim_thompson5910
so you have to make a completely different scenario?
JozelynW
  • JozelynW
no just use the scenario from part 2 to make up a question
JozelynW
  • 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
  • JozelynW
but I don't know what numbers are suppose to be in the geometric series here is the example
1 Attachment
jim_thompson5910
  • 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
  • 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
  • JozelynW
is it like the example?
jim_thompson5910
  • jim_thompson5910
yes
JozelynW
  • JozelynW
ok than so what would be the geometric series than for the question?
jim_thompson5910
  • jim_thompson5910
I'm not sure what you're asking exactly?
JozelynW
  • 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
  • JozelynW
I think it means 3 numbers that have a common ratio of 5%
jim_thompson5910
  • jim_thompson5910
you mean they want you to add up the first three terms of the geometric sequence?
JozelynW
  • JozelynW
idk honestly. I'm just listening to you
JozelynW
  • JozelynW
does it look like what it mean in the picture
JozelynW
  • JozelynW
this is a project and it doesn't really explain much
jim_thompson5910
  • 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
  • JozelynW
So the question would be "Find the sum of the first 7 terms
jim_thompson5910
  • jim_thompson5910
yes the work shown above would apply to that question
JozelynW
  • JozelynW
Thank you, your name should say lifesaver. You just helped me finish out my math class.
jim_thompson5910
  • jim_thompson5910
I'm glad I could be of help

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