A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 one year ago
Help with arithmetic?
anonymous
 one year ago
Help with arithmetic?

This Question is Closed

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@uri @SolomonZelman @mathstudent55

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0What are the explicit equation and domain for an arithmetic sequence with a first term of 5 and a second term of 2?

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.2An arithmetic sequence has a common difference. Since the second term is 2 and the first term is 5, the common difference is 2  5 = 3 When you add the common difference to a term, you get the next term.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.25 5 + ( 3) = 2 2 + ( 3) = 1 1 + ( 3) = 4 4 + (3) = 7 The first 5 terms of the sequence are: 5, 3, 1, 4, 7

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.2Since adding 3 is the same as subtracting 3, you can eliminate the first two choices because in those choices, you are subtracting multiples of 2. We need to subtract multiples of 3 to find subsequent terms. The answer has to be choice C or choice D.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Right! Wow this is making so much more sense than I thought it would

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.2To figure out which one it is, look at choice C. \(a_n = 5  3(n  1)\) for all integers n, such that \(n \ge 0\)

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.2Use the equation of choice C., and plug in the first value of n. That would be n = 0. \(a_n = 5  3(n  1)\) \(a_0 = 5  3(0  1)\) What value do you get for \(a_0\) ?

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.2Correct. According to choice C., the first term in the sequence is called \(a_0\), and it is 8. We were told the first term is 5, so choice C cannot be correct.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.2Wait. I got the two choices confused. I did choice D above, where n>= 0. Choice D. is eliminated.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.2Now let's look at choice C., which is C. \(a_n = 5  3(n  1)\) for all integers n, such that \(n \ge 1\) \(a_n = 5  3(n  1)\) \(a_1 = 5  3(1  1)\) Now for choice C., what do you get for the first term?

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.2Correct. Choice C. gives us the correct first term. Now notice what happens as n becomes 2, then 3, then 4, etc. Each time you are subtracting 1 from the next integer, then multiplying it by 3. That means first you subtract 0 from 5 (what you did for term 1) Then you subtract 3 from 5, then you subtract 6 from 5, then you subtract 9 from 5, etc. giving you the terms of the sequence. The answer is C.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Okay, got it! Makes total sense. Thank you so SO much!

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Is my answer right with this one? It's a similar problem. @mathstudent55

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.2Let's see. Choice D. starts with n = 0. What do you get when you replace n with 0 below? \(a_n = 4(12)^{n  1} \) \(a_0 = 4(12)^{0  1} \) What is \(a_0\) ?

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.2\(a_0 = 4(12)^{0  1} = 4 (12)^{1} = \dfrac{4}{12} = \dfrac{1}{3}\) Correct. We are told the first term is 4. That means this cannot be the answer.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Yeah, I was hesitant on my answer. Glad I checked!

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So it would be C., correct?

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.2In the previous problem we had an arithmetic sequence. Notice this is a geometric sequence. Do you know the difference between a geometric sequence and an arithmetic sequence?

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.2In an arithmetic sequence (as we saw in the earlier problem) there is a common difference. If you add the common difference to a term, you get the next term. To find the common difference, subtract a term from the next term. In a geometric sequence there is a common ratio. If you multiply a term by the common ratio, you get the next term. To find the common ratio, divide a term by the previous term.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.2Look at the first term and the second term: 4 and 8. What is 8/4 = ?

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.2Right. The common ratio is 2, so you need an equation with a 2. That means we need A. or B.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0The sequence follows by 8, 16, 32, 64 . . .

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.2B. is correct because it gives us the correct first term, 4.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Okay, just asking, but why wouldn't it be A.?

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.2Let's look at A. \(a_n =4(2)^{n  1} \); \(n \ge 0\) The first term uses n = 0: \(a_0 =4(2)^{0  1} \) What is \(a_0\) using choice A.?

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.2Right, but we were told the first term is 4, so A. cannot be correct.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Ooo okay. Got it! Thank you so much!

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I got 100%!! Thanks so much!
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.