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Arithmetic or geometric sequence

I am a little confused by the layout of this question here:

IMG_0849.jpeg


I believe it’s asking for the value of the arithmetic series for the first 4 terms, however; I am finding that,

U₁=6 ,U₂=59, U₃=536, U₄=4829… doesn’t look like an arithmetic sequence to me as there’s no common difference. Yet, the sigma notation refers to arithmetic summation.

Am I having a moment here?
(edited 1 month ago)
Reply 1
Original post by KingRich
I am a little confused by the layout of this question here:
IMG_0849.jpeg
I believe it’s asking for the value of the arithmetic series for the first 4 terms, however; I am finding that,
U₁=6 ,U₂=59, U₃=536, U₄=4829… doesn’t look like an arithmetic sequence to me as there’s no common difference. Yet, the sigma notation refers to arithmetic summation.
Am I having a moment here?

If it was
u_(n+1) = u_n + 5
then it would be an arithmetic sequence as 5 is the common difference. If it was
u_(n+1) = 9u_n
then it would be a geometric sequence as the common ratio is 9.

So this question is a combination of the two and the easiest thing to do is simply evaluate the sequence and sum the values.
Reply 2
Original post by mqb2766
If it was
u_(n+1) = u_n + 5
then it would be an arithmetic sequence as 5 is the common difference. If it was
u_(n+1) = 9u_n
then it would be a geometric sequence as the common ratio is 9.
So this question is a combination of the two and the easiest thing to do is simply evaluate the sequence and sum the values.

I see. So, there’s no common difference or common ratio as it’s a combination. So, my terms are correct based on the term to term rule, inputting the previous term to find the next term.

I just have to sum those terms? To be 5430.
Reply 3
Original post by KingRich
I see. So, there’s no common difference or common ratio as it’s a combination. So, my terms are correct based on the term to term rule, inputting the previous term to find the next term.
I just have to sum those terms? To be 5430.

Ive not checked your numbers, but assuming you can use a calc so ...
Reply 4
Original post by mqb2766
Ive not checked your numbers, but assuming you can use a calc so ...

😅😅 oh man, it would suck if I couldn’t lol. It wouldn’t be the first that I’ve rushed and missed a number though
Reply 5
Original post by KingRich
😅😅 oh man, it would suck if I couldn’t lol. It wouldn’t be the first that I’ve rushed and missed a number though

Just to go back to the OP, you refer to the sigma/summation symbol and seem to relate that to an arithmetic sequence? Really its just saying sum the terms in the sequence, whatever type of sequence it is. So if its an xxx sequence, then the summation symbol means youre evaulating an xxx series. Though knowing the sequence/series type is fairly irrelevant for this quesiton where they seem to want you to do the numbers rather than apply a formula.
(edited 1 month ago)
Reply 6
Original post by mqb2766
Just to go back to the OP, you refer to the sigma/summation symbol and seem to relate that to an arithmetic sequence? Really its just saying sum the terms in the sequence, whatever type of sequence it is. So if its an xxx sequence, then the summation symbol means youre evaulating an xxx series. Though knowing the sequence/series type is fairly irrelevant for this quesiton where they seem to want you to do the numbers rather than apply a formula.

Yeah I do because after the sigma there’s Un, which In the material they provide refer’s to an arithmetic series, either that or an Xn.

For geometric series, they used a sigma notation followed by ar^n-1..

So, is it irrelevant what’s after the sigma? Un alone can refer to geometric or arithmetic? Just a sum of all the terms regardless of the type of sequence?
Reply 7
Original post by KingRich
Yeah I do because after the sigma there’s Un, which In the material they provide refer’s to an arithmetic series, either that or an Xn.
For geometric series, they used a sigma notation followed by ar^n-1..
So, is it irrelevant what’s after the sigma? Un alone can refer to geometric or arithmetic? Just a sum of all the terms regardless of the type of sequence?

For this question the summation means sum the terms in the sequence which is pretty much the definition of the corresponding series. If youve got another interpretation of what youre doing with a summation, just post it.
Reply 8
Original post by mqb2766
For this question the summation means sum the terms in the sequence which is pretty much the definition of the corresponding series. If youve got another interpretation of what youre doing with a summation, just post it.

Looking back at my notes I now believe I understand my misunderstanding….

So, for an arithmetic nth term Un=a+(n-1)d and geometric nth term Un=ar^n-1….

In the case of sigma logo.

IMG_0852.jpeg

It doesn’t have to specify the argument, it may just state Un which would refer to the sum of either the arithmetic series or geometric series.

As for this questions as it’s a combination of both geometric and arithmetic, finding the nth term isn’t something that’s straight forward without knowing r or d. Or, at least, I’m unaware how to do so in this format.
Reply 9
Original post by KingRich
Looking back at my notes I now believe I understand my misunderstanding….
So, for an arithmetic nth term Un=a+(n-1)d and geometric nth term Un=ar^n-1….
In the case of sigma logo.
IMG_0852.jpeg
It doesn’t have to specify the argument, it may just state Un which would refer to the sum of either the arithmetic series or geometric series.
As for this questions as it’s a combination of both geometric and arithmetic, finding the nth term isn’t something that’s straight forward without knowing r or d. Or, at least, I’m unaware how to do so in this format.

Pretty much that. Summing a whatever sequence is a whatever series and you can write the series as 1+2+3+... or use the summation symbol.

It isnt too hard to adapt the basic arithmetic/geometric series ideas for this question, but its beyond what is required.
Reply 10
Original post by mqb2766
Pretty much that. Summing a whatever sequence is a whatever series and you can write the series as 1+2+3+... or use the summation symbol.
It isnt too hard to adapt the basic arithmetic/geometric series ideas for this question, but its beyond what is required.

Oh, completely off topic by the way. Seeing as you’re the only person that I tend to talk to in correspondence to my further studies. I thought you'd be interested to know that I got my recent feedback from my assignment Atomic Structure and Periodic Table and received a distinction.

Being someone in school who only ever got D's and only ever B in Art, I'm proud of myself but have no one else to gloat to lol
Original post by KingRich
Oh, completely off topic by the way. Seeing as you’re the only person that I tend to talk to in correspondence to my further studies. I thought you'd be interested to know that I got my recent feedback from my assignment Atomic Structure and Periodic Table and received a distinction.
Being someone in school who only ever got D's and only ever B in Art, I'm proud of myself but have no one else to gloat to lol
Well done, must be getting more intelligent as you get older. Tbh, a B in art sounds fairly impressive compared to my (lack of) efforts.
Reply 12
Original post by mqb2766
Well done, must be getting more intelligent as you get older. Tbh, a B in art sounds fairly impressive compared to my (lack of) efforts.

😅 I’m naturally creative. Art to me comes to me as easy as making toast. It just doesn’t keep my mind occupied long enough, so I become bored very quickly. Partly why I pursued carpentry, for the creative side but you sorta need money to buy the machinery which I don’t have lol

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