Question

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)

Answer 1

@dan815

Answer 2

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

Answer 3

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

Answer 4

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.

Answer 5

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

Answer 6

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

Answer 7

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

Answer 8

ok what sequence did you make up on your own?

Answer 9

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

Answer 10

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

Answer 11

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

Answer 12

it says `Jasmine practices the piano for 20 minutes on Monday`

so the first term of this sequence is 20
making a = 20

Answer 13

the next day, tuesday, would be

a+d = 20+4 = 24 min

-------------------------

wednesday would be

24+4 = 28

etc etc

Answer 14

so how would that be written

Answer 15

a = 20 and d = 4

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

Answer 16

so,

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

Answer 17

thank you for you help.

Answer 18

glad to be of help

Answer 19

@jim_thompson5910 need you help again with another 1

Answer 20

go ahead

Answer 21

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

Answer 22

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

Answer 23

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

Answer 24

`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

Answer 25

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

Answer 26

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

Answer 27

then what would i do

Answer 28

the first term is a = 45

the common ratio is r = 0.05 (decimal form of 5%)

Answer 29

no sorry, the common ratio would be 1.05

1+0.05 = 1.05

Answer 30

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

Answer 31

first term: 45

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

etc etc

Answer 32

change the 5% to 1.05%?

Answer 33

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

Answer 34

the nth term should be

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

Answer 35

ok

Answer 36

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

Answer 37

the x= times

Answer 38

the exponent should be n-1 = 4-1

so

\[\LARGE a_4 = 45*(1.05)^{4-1}\]

Answer 39

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

Answer 40

so 5-1

Answer 41

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

Answer 42

yes it's a5 not a4

Answer 43

they wanted me to find a5 the fifth term.

Answer 44

I see

Answer 45

ok so the answer would be what i said rightttt

Answer 46

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

Answer 47

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

Answer 48

ok

Answer 49

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

Answer 50

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 51

I think you meant to write

\[\LARGE a_5 = 45 \times 1.05^{5-1}\] right?

Answer 52

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

Answer 53

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

Answer 54

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 `\[` and `\]`

Answer 55

as for the summation formula, it would be

\[\Large S_n = a*\frac{1-r^n}{1-r}\]

Answer 56

which is equivalent to the form you wrote

Answer 57

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

Answer 58

yes the two are equivalent

\[\Large S_n = a*\frac{1-r^n}{1-r} = \frac{a-a*r^n}{1-r}\]

Answer 59

I'm going to screenshot it

Answer 60

yeah which is what I wrote here

\[\Large S_n = \frac{a-a*r^n}{1-r}\]

Answer 61

there are 2 versions of the same thing really

Answer 62

ok

Answer 63

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

Answer 64

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

Answer 65

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

Answer 66

you can use another value of n

Answer 67

ok 5

Answer 68

Oh it says use the same scenario

Answer 69

from part 2

Answer 70

so a = 45 and r = 1.05

Answer 71

right ,but i need to make a question now

Answer 72

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

Answer 73

so you have to make a completely different scenario?

Answer 74

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

Answer 75

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

Answer 76

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

Answer 77

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

Answer 78

\[\Large S_n = \frac{a-a*r^n}{1-r}\]

\[\Large S_5 = \frac{45-45*1.05^5}{1-1.05}\]

\[\Large S_5 = ???\]

Answer 79

is it like the example?

Answer 80

yes

Answer 81

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

Answer 82

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

Answer 83

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

Answer 84

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

Answer 85

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

Answer 86

idk honestly. I'm just listening to you

Answer 87

does it look like what it mean in the picture

Answer 88

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

Answer 89

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

Answer 90

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

Answer 91

yes the work shown above would apply to that question

Answer 92

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

Answer 93

I'm glad I could be of help