Arithmetic Concepts: Get Help Understanding Problems

[Coder74]

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!

View attachment 6475

 

[Euge]

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 $a_5$.

 

[Coder74]

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.

 

[MarkFL]

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