Final answer:
To find the number of terms in the arithmetic sequence 18, 15 1/2, 13, ..., -47, we calculate the common difference and apply the formula for the nth term. We solve for the number of terms n, which results in n = 27, meaning there are 27 terms in the sequence.
Step-by-step explanation:
To find the number of terms in the arithmetic progression series 18, 15 1/2, 13, ..., -47, we use the formula for the nth term of an arithmetic sequence, which is:
an = a1 + (n - 1)d, where an is the nth term, a1 is the first term, d is the common difference, and n is the number of terms.
The first term a1 = 18 and the second term is 15 1/2, so the common difference d is 15 1/2 - 18 = -2 1/2 or -2.5. We set the nth term equal to -47 and solve for n:
-47 = 18 + (n - 1)(-2.5).
To find n, we rearrange and solve the equation:
-47 - 18 = (n - 1)(-2.5)
-65 = (n - 1)(-2.5)
n - 1 = 26
n = 27.
Therefore, the number of terms in the arithmetic progression is 27.