Understanding Arithmetic Sequences: Tips and Strategies

[doreent0722]

Need help on these questions I haven't been introduced yet. Please look at image I inserted in.

 

[Jameson]

Need help on these questions I haven't been introduced yet. Please look at image I inserted in.

Hi doreent0722,

Welcome to MHB! :)

I don't see any images. Can you try typing one out or uploading them to a site like imgur.com?

 

[doreent0722]

Hi doreent0722,

Welcome to MHB! :)

I don't see any images. Can you try typing one out or uploading them to a site like imgur.com?

1). {2 + 5/N} FIND THE SEVENTH AND ELEVENTH TERMS OF THE SEQUENCE?
2). A1: A8=31, A9=34 FIND THE SPECIFIED TERM OF THE ARITHMETIC SEQUENCE THAT HAS THE TWO GIVEN TERMS.
3). A7 =1/3, D= -2/3, N=15 FIND THE SUM OF THE ARITHMETIC SEQUENCE Sn THAT SATISFIES THE STATED CONDITIONS

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Hi doreent0722,

Welcome to MHB! :)

I don't see any images. Can you try typing one out or uploading them to a site like imgur.com?

I tried to post it on imgur.com but because image is too large it will not go thru. I did send you the questions on the image.

 

[Jameson]

Ok, thank you for posting. First thing is, no need TO SHOUT :) We can read just fine.

What have you tried for the first question? We ask that you post one question at a time.

Is that $\displaystyle 2+\frac{5}{N}$ or $\displaystyle \frac{2+5}{7}$? I'm guessing the first one.

Let $N=1$ what do you get for the result?

 

[doreent0722]

Ok, thank you for posting. First thing is, no need TO SHOUT :) We can read just fine.

What have you tried for the first question? We ask that you post one question at a time.

Is that $\displaystyle 2+\frac{5}{N}$ or $\displaystyle \frac{2+5}{7}$? I'm guessing the first one.

Let $N=1$ what do you get for the result?

Sorry for the caps its an OCD habit. I'm not yelling at you it just looks to me nicer.
I haven;t tried anything on those questions for yesterday was my first day in class for Algebra & trigonometry. Once again I'm so Sorry for the caps lettering. Will you please tutor on all of those questions so I can learn for my Monday class?

 

[Jameson]

Sorry for the caps its an OCD habit. I'm not yelling at you it just looks to me nicer.
I haven;t tried anything on those questions for yesterday was my first day in class for Algebra & trigonometry. Once again I'm so Sorry for the caps lettering. Will you please tutor on all of those questions so I can learn for my Monday class?

No worries about the caps. Now you know our custom. :)

I will try to help you figure it out but we don't give out answers so we're going to have to do this together.

You didn't comment on the two choices in my last post but let's assume that the sequence we have is:

$\displaystyle 2+\frac{5}{N}$

Ok let's start with $N=1$

$\displaystyle 2+\frac{5}{1}=2+5=7$. So the first term is 7.

If I want to find the third term, I plug in $N=3$.

$\displaystyle 2+\frac{5}{3}=\frac{6}{3}+\frac{5}{3}=\frac{11}{3}$

Using the same method, how would you get the 7th and 11th terms?

 

[MarkFL]

I'll start at the other end and help with the third problem:

[box=blue]3). \(\displaystyle a_7 =\frac{1}{3}\), \(\displaystyle d= -\frac{2}{3}\), \(\displaystyle n=15\).
Find the sum of the arithmetic sequence $S_n$ that satisfies the stated conditions.[/box]

Okay, we will find helpful the following formula:

[box=red]

Sum Of Arithmetic Progression​

---

\(\displaystyle S_n=\frac{n}{2}\left(2a_1+(n-1)d\right)\tag{1}\)[/box]

We are given $n$ and $d$, and we need to find $a_1$. Every time we reduce the index by 1 we increase the value of the term by $-d$. So, to get to $a_1$, we decrease the index by how much from $a_7$, and therefore, how much should be added to $a_7$ to get the value of $a_1$?

 

[doreent0722]

No worries about the caps. Now you know our custom. :)

I will try to help you figure it out but we don't give out answers so we're going to have to do this together.

You didn't comment on the two choices in my last post but let's assume that the sequence we have is:

$\displaystyle 2+\frac{5}{N}$

Ok let's start with $N=1$

$\displaystyle 2+\frac{5}{1}=2+5=7$. So the first term is 7.

If I want to find the third term, I plug in $N=3$.

$\displaystyle 2+\frac{5}{3}=\frac{6}{3}+\frac{5}{3}=\frac{11}{3}$

Using the same method, how would you get the 7th and 11th terms?

I'm sorry I don't know how to do this. Will you please show me how to by step by step to solve it.

 

[doreent0722]

I'll start at the other end and help with the third problem:

[box=blue]3). \(\displaystyle a_7 =\frac{1}{3}\), \(\displaystyle d= -\frac{2}{3}\), \(\displaystyle n=15\).
Find the sum of the arithmetic sequence $S_n$ that satisfies the stated conditions.[/box]

Okay, we will find helpful the following formula:

[box=red]

Sum Of Arithmetic Progression​

---

\(\displaystyle S_n=\frac{n}{2}\left(2a_1+(n-1)d\right)\tag{1}\)[/box]

We are given $n$ and $d$, and we need to find $a_1$. Every time we reduce the index by 1 we increase the value of the term by $-d$. So, to get to $a_1$, we decrease the index by how much from $a_7$, and therefore, how much should be added to $a_7$ to get the value of $a_1$?

Thanks so far but how do I solve for my answer?

 

[MarkFL]

I'm sorry I don't know how to do this. Will you please show me how to by step by step to solve it.

Jameson has showed you exactly what you need to do...the $n$th term, or $a_n$ is given by:

\(\displaystyle a_n=2+\frac{5}{n}\)

So, if you are given a value for $n$, you just plug it in where you see $n$...for example:

\(\displaystyle a_2=2+\frac{5}{2}=\frac{4+5}{2}=\frac{9}{2}\)

Now, can you do the same thing, only for $n=7$ and $n=11$?

 

[MarkFL]

Thanks so far but how do I solve for my answer?

You need to find $a_1$...how many steps do you have to take back to get from $a_7$ to $a_1$?

 

[doreent0722]

You need to find $a_1$...how many steps do you have to take back to get from $a_7$ to $a_1$?

Sorry this is my first homework from class yesterday. Instructor gave it to us to see where our weakness is and its also to be good on our behalf.

 

[MarkFL]

Sorry this is my first homework from class yesterday. Instructor gave it to us to see where our weakness is and its also to be good on our behalf.

Suppose you number the steps in a staircase, starting with the number 1 for the first step, and number 2 for the second and so on. Now suppose you are on step number 7...how many steps down do you have to take to get to step number 1?

 

[Jameson]

You're basically just saying you can't do any of this and you want answers. It's ok to not know how to do something. :) We all start somewhere but we aren't going to give you the answer. If the purpose of this assignment is to assess your level then you should be honest that you are stuck and not turn in work that indicates you know more than you do.

If you get some basic background on these topics and can explain where you are stuck, we would be glad to help you through it but right now we don't know what you understand and what you don't. "I don't understand" is hard to work with.

Let me try it this way. Have you taken a class with algebra before? How comfortable do you feel with fractions?