Final answer:
The list is an arithmetic sequence with -36 as the first term and 48 as the last term, with a common difference of 7. Using the formula for the nth term of an arithmetic sequence, we find that there are 15 terms in the list.
Step-by-step explanation:
The student's question is about determining the number of numbers in the given list from -36 to 48 with a common difference. This type of question involves the use of arithmetic sequences, which is a sequence of numbers where the difference between consecutive terms is constant.
To find the number of terms in the sequence, we use the formula for the nth term of an arithmetic sequence, which is a_n = a_1 + (n - 1)d, where a_n is the last term, a_1 is the first term, d is the common difference, and n is the number of terms.
Substituting the values (-36 for a_1, 48 for a_n, and 7 for d), we'll solve for n:
48 = -36 + (n - 1)7
48 + 36 = (n - 1)7
84 = (n - 1)7
n - 1 = 84 / 7
n - 1 = 12
n = 13
However, this does not take into account that the sequence had started from -36, which means we need to adjust our count by adding both the first and last term to the count of numbers between them. Thus, the total number of terms in the sequence is 13 + 2 = 15.