Find the number of terms in an AP given that its first term and last terms are 13 and -23 respectively and that its common difference is -2¼
The formula to find the number of terms in an arithmetic progression is:
Number of terms = (last term - first term) / common difference + 1.
Given that the first term is 13, the last term is -23, and the common difference is -2¼ (or -9/4), we can substitute these values into the formula:
Number of terms = (-23 - 13) / (-9/4) + 1
Number of terms = (-36) / (-9/4) + 1
Number of terms = (-36) * (4/(-9)) + 1
Number of terms = 16 + 1
Number of terms = 17.
Therefore, there are 17 terms in the arithmetic progression.