MHB Arithmetic Concepts: Get Help Understanding Problems

AI Thread Summary
The discussion focuses on solving a recursive arithmetic problem using the formula $a_n = 3a_{n-1} + 2$. The user seeks clarification on calculating terms in the sequence, starting with $a_2$ and $a_3$, based on the initial value $a_1 = 1$. Another participant highlights the difference between recursive and closed-form problems, providing an example for clarity. The conversation emphasizes the importance of understanding the structure of the problem to find solutions effectively. Overall, the thread serves as a collaborative effort to assist with arithmetic concepts and problem-solving strategies.
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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