given the first term is - 14, from which we can say that a = - 14

To find: the number of terms in an AP whose first and fifth terms is - 14 and 2 respectively, and the sum of the terms is 40

Given fifth term is 2, so a + 4d = 2

- 14 + 4d = 2

d = 4

we know that the sum of AP is given by the formula:

now substituting the values in the above equation

4n² - 32n - 80 = 0

n² - 8n - 20 = 0

solving we get n as 10 or - 2

Since the number of terms cannot be negative hence n is 10