How do you find terms in a sequence?

Question

anonymous · Answer

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mathstudent55 · Answer

This sequence needs the previous two terms to determine a term.
$a_{n - 1} $ is the previous term, and $a_{n - 2} $ is the term before the previous term.

mathstudent55 · Answer

You are given the first two terms, $a_1$ and $a_2$.
Use those terms to find the third term.
Then use the second and third terms to find the fourth term, etc.

solomonzelman · Answer

do you experience any difficulty reading the notations in your question, like $\large\color{black}{ b_3   }$ and all that stuff?

anonymous · Answer

It doesn't line up when I plug in the terms given :/

mathstudent55 · Answer

$\large b_n = -3b_{n - 2} + 5b_{n - 1} $

We want $b_3$, so we use n = 3.
That means $b_{n - 2} = b_1$, and $b_{n - 1} = b_2$.

mathstudent55 · Answer

$\large b_n = -3b_{n - 2} + 5b_{n - 1} $

$\large \color{red} {b_1 = -1}$; $\large \color{green}{b_2 = 6}$

$\large \color{blue}{b_3} = -3\color{red}{b_1} + 5\color{green}{b_2} = -3\color{red}{(-1)} + 5\color{green}{(6)} = \color{blue}{33} $

$\large b_4 = -3b_{4 - 2} + 5b_{4 - 1}  = -3\color{green}{b_{2}} + 5\color{blue}{b_{3}} =  $              etc.

anonymous · Answer

@mathstudent55 so my answer's A?

mathstudent55 · Answer

Yes. Even without calculating b4 and b5, the answer must be A because choice A is the only one that has the correct b3 term.