Question 9

Explanation

Given the recursive formula of the sequence is $b_{n+2} = b_{n+1} - 3b_n$. We also know the values $b_4 = 5$ and $b_5 = -1$. We are asked to find the value of $b_2$. We will find it by working backwards from $b_5$ to $b_3$, and then to $b_2$.

Finding the Value of b3

Use the formula with $n = 3$:

Substitute the values $b_5 = -1$ and $b_4 = 5$:

Finding the Value of b2

Use the formula with $n = 2$:

Substitute the values $b_4 = 5$ and $b_3 = 2$:

So, the value of $b_2$ is $-1$.