Answer:

the missing values and the arithmetic mean for each sequence are as follows:

1. -34, -20.5, -20.5, -7

2. 2a, (29a / 6), (29a / 6), (29a / 6), (29a / 6), 27a

3. -9, (17 / 6), (17 / 6), (17 / 6), (17 / 6), 26

Step-by-step explanation:

To find the missing values in each sequence and calculate the arithmetic mean, we need to determine the pattern and find the values that fill the gaps.

1. -34, ____, _____, -7

To find the missing values, we can calculate the arithmetic mean of the given numbers:

(-34 + -7) / 2 = -41 / 2 = -20.5

So, the missing values are -20.5 and -20.5.

2. 2a, __, ___, ____, ____, 27a

To find the missing values, we can calculate the arithmetic mean of the given numbers:

(2a + 27a) / 6 = 29a / 6

The missing values are (29a / 6), (29a / 6), (29a / 6), and (29a / 6).

3. -9, __, ___, ____, ____, 26

To find the missing values, we can calculate the arithmetic mean of the given numbers:

(-9 + 26) / 6 = 17 / 6

The missing values are (17 / 6), (17 / 6), (17 / 6), and (17 / 6).

So, the missing values and the arithmetic mean for each sequence are as follows:

1. -34, -20.5, -20.5, -7

2. 2a, (29a / 6), (29a / 6), (29a / 6), (29a / 6), 27a

3. -9, (17 / 6), (17 / 6), (17 / 6), (17 / 6), 26