Find the 8th term of the arithmetic sequence 5x + 7, x +12, -3x + 17
To find the 8th term of the arithmetic sequence 5x + 7, x +12, -3x + 17, we first need to determine the common difference, which is the difference between consecutive terms in the sequence.
The common difference (d) can be found by subtracting the second term from the first term:
d = (x + 12) - (5x + 7)
= x + 12 - 5x - 7
= -4x + 5
Now that we know the common difference (d = -4x + 5), we can find the 8th term using the formula for the nth term of an arithmetic sequence:
An = A1 + (n - 1) * d
Here, A1 represents the first term, d is the common difference, and n is the term number we want to find (in this case, n = 8).
Substituting the given values into the formula:
A8 = (5x + 7) + (8 - 1) * (-4x + 5)
= 5x + 7 + (7) * (-4x + 5)
= 5x + 7 - 28x + 35
= -23x + 42
Therefore, the 8th term of the arithmetic sequence is -23x + 42.