Answer
$a_2 = -4$
$a_3 = -10$
$a_4 = -16$
Work Step by Step
With arithmetic sequences, the middle term of three consecutive terms can be found by taking the arithmetic mean of the two terms that are given.
For this exercise, we can use the third term as the middle term. If we take the arithmetic mean of the first and fifth terms, then we will get the third term.
The arithmetic mean is given by the formula:
arithmetic mean = $\frac{x + y}{2}$
Substitute the first and fifth terms into the formula:
arithmetic mean = $a_3 = \frac{2 + (-22)}{2}$
Add to simplify:
arithmetic mean = $a_3 = \frac{-20}{2}$
Simplify the fraction:
arithmetic mean = $a_3 = -10$
To find the second term, $a_2$, apply the arithmetic mean formula again, using the first and third terms:
$a_2 = \frac{2 + (-10)}{2}$
Add to simplify:
$a_2 = \frac{-8}{2}$
Simplify the fraction:
$a_2 = -4$
To find the fourth term, $a_4$, apply the arithmetic mean formula again, using the third and fifth terms this time:
$a_4 = \frac{-10 + (-22)}{2}$
Add to simplify:
$a_4 = \frac{-32}{2}$
Simplify the fraction:
$a_4 = -16$
