Arithmetic Concepts: Get Help Understanding Problems

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    Arithmetic Concepts
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Discussion Overview

The discussion revolves around understanding arithmetic concepts, specifically focusing on solving recursive equations and transitioning to closed forms. Participants seek clarification on problem-solving techniques and approaches to similar arithmetic problems.

Discussion Character

  • Homework-related
  • Mathematical reasoning

Main Points Raised

  • One participant expresses confusion about a recursive formula and seeks help in understanding how to apply it to find specific terms.
  • Another participant provides a step-by-step approach to calculating terms in the recursion, demonstrating how to find $a_2$ and $a_3$ using the given formula.
  • A different participant mentions a related question that lacks substitution terms and asks for guidance on how to start solving it.
  • One participant points out that the example provided involves a closed form and suggests using a specific value for $n$ to find the answer.
  • A later reply advises starting a new thread for unrelated problems, indicating a preference for organized discussions.

Areas of Agreement / Disagreement

Participants generally agree on the need for clarification and assistance with arithmetic problems, but there are multiple approaches to solving the problems presented, and the discussion remains unresolved regarding the best methods for different types of questions.

Contextual Notes

Some participants may have different levels of familiarity with recursion and closed forms, which could affect their understanding of the problems. Additionally, the transition from recursive to closed-form solutions may not be straightforward for all participants.

Coder74
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Hi everyone!
I'm having trouble solving this problem, its set up in a way that I don't understand and I was hoping someone could help clarify it with me..Thanks a bunch!

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Hi Coder74,

Let's first find $a_2$. To do so, set $n = 2$ in the recursion formula $a_n = 3a_{n-1} + 2$ to get $a_2 = 3a_1 + 2$. It's given that $a_1 = 1$, so $a_2 = 3(1) + 2 = 5$. Now consider $a_3$. Set $n = 3$ in the recursion formula to get $a_3 = 3a_2 + 2 = 3(5) + 2 = 17$. Continue to $a_5$.
 
Thanks so much!
I have a similar question but this doesn't have any terms to be substituted like the above equation.. How do I go about starting this? I've been sitting here like a bump on a log for a while and my teacher has gone offline..(I'm homeschooled)
I really appreciate everyone and their hard work on this website!

Example: View attachment 6481

This is a practice question I sampled from the extra help section..it looks exactly like the one I'm having trouble with but it looked a little easier.
 

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In this example, you are given the closed form, rather than a recursion, so you simply need to use $n=10$, that is:

$$a_{10}=2(-1)^{10}=?$$

In the future, please begin a new thread for a new problem. :D
 

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