Problem 19

Explanation

We are given a recursive formula for a sequence of numbers:

We also know that $a_1 = -1$ and $a_2 = 2$. We are asked to find the value of $a_4 + a_1$.

Determining the Value of the Fourth Term

To find $a_4$, we can use the given equation by substituting $n = 1$:

Next, we substitute the values $a_1 = -1$ and $a_2 = 2$ into the equation:

Calculating the Sum

Now that we have found $a_4 = -1$, we can calculate $a_4 + a_1$:

So, the value of $a_4 + a_1$ is $-2$.