Final answer:
To find the tenth element of an arithmetic sequence with a first element of 8 and a third element of 2, we can use the formula for arithmetic sequence. By substituting the known values and solving for the common difference, we find that the common difference is -3. Using this common difference, we can then find the tenth element as -19.
Step-by-step explanation:
To find the tenth element of an arithmetic sequence, we need to first determine the common difference. We know that the first element is 8 and the third element is 2.
Using the formula for arithmetic sequence: an = a1 + (n-1)d, where an is the nth element, a1 is the first element, n is the position of the element, and d is the common difference.
Let's substitute the known values:
a3 = a1 + (3-1)d => 2 = 8 + 2d
Now, solve for d:
2d = -6 => d = -3
Now that we know the common difference is -3, we can find the tenth element:
a10 = a1 + (10-1)d => a10 = 8 + 9(-3) = 8 - 27 = -19.