The first and fifth terms of an A.P. are -14 and 2 respectively and the sum of its n terms is 40 . The value of n is

Step-by-step solution

Let the first term of the arithmetic progression be a and the common difference be d . Given a = -14 and the fifth term a₅ = a + 4d = 2 . Substituting a = -14 into the equation a + 4d = 2 : -14 + 4d = 2 4d = 16 d = 4 . The sum of n terms of an A.P. is given by S_n = n 2 [2a + (n - 1)d] . Given S_n = 40 , we have 40 = n 2 [2(-14) + (n - 1)4] . 80 = n [-28 + 4n - 4] . 80 = n [4n - 32] . 80 = 4n^2 - 32n . n^2 - 8n - 20 = 0 . Factoring the quadratic equation: (n - 10)(n + 2) = 0 . Since n must be a positive integer, n