Answer:
The tenth term is -14.
Explanation:
To find the pattern and the tenth term, we need to first figure out the sequence to which these numbers belong. From the given numbers, it is not immediately clear what the sequence is, as they seem to be a random collection of integers and fractions.
One possible way to approach this problem is to look at the differences between consecutive terms in the sequence, as this can reveal a pattern.
Starting with the second term, we have:
-6 - (-2) = -4
-2 - 0 = -2
0 - 1 = -1
1 - 3/2 = -1/2
We notice that the differences are all negative, and they are all either -1 or -1/2. This suggests that the sequence is a decreasing arithmetic sequence, with a common difference of -1 or -1/2.
To confirm this, we can try to extend the sequence using the pattern we have found. Let x be the first term in the sequence, and let d be the common difference. Then the sequence can be written as:
x, x - d, x - 2d, x - 3d, ...
We know the values of the first four terms, so we can use them to solve for x and d:
x = -6 + d
x - d = -2
x - 2d = 0
x - 3d = 1
Subtracting the second equation from the first, we get:
2d = -4
So d = -2.
Substituting this value of d into the third equation, we get:
x - 2(-2) = 0
Solving for x, we get:
x = 4
So the sequence is:
4, 2, 0, -2, -4, -6, -8, -10, -12, -14, ...
The tenth term is -14.