Answer
$a_4 = -12.5$
$a_5 = -8$
$a_6 = -3.5$
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 fifth term as the middle term. If we take the arithmetic mean of the third and seventh terms, then we will get the third term.
The arithmetic mean is given by the formula:
arithmetic mean = $\frac{x + y}{2}$
Substitute the third and seventh terms into the formula:
arithmetic mean = $a_5 = \frac{-17 + 1}{2}$
Add to simplify:
arithmetic mean = $a_5 = \frac{-16}{2}$
Simplify the fraction:
arithmetic mean = $a_5 = -8$
To find the fourth term, $a_4$, apply the arithmetic mean formula again, using the third and fifth terms:
$a_4 = \frac{-17 + (-8)}{2}$
Add to simplify:
$a_4 = \frac{-25}{2}$
Simplify the fraction:
$a_4 = -12.5$
To find the sixth term, $a_6$, apply the arithmetic mean formula again, using the fifth and seventh terms this time:
$a_6 = \frac{-8 + 1}{2}$
Add to simplify:
$a_6 = \frac{-7}{2}$
Simplify the fraction:
$a_6 = -3.5$
