Question

The first term of an A.P is 3 and the fifth term is 9.Find the number of
terms in the progression if the sum of the progression is 81.

Answer 1

there are 4 differences between 3 and 9 ... d = (9 - 3) / 4 = 3/2

for n terms , the sum is ... 3 n + [d (n - 1) (n / 2)] = d/2 n^2 + (3 - d/2) n = 81

3/4 n^2 + 9/4 n - 81 = 0

use the quadratic formula to find n

Answer 2

n/2 (3+(n-1)(3/2)) = 81
1/4 (3n^2+3n-324) = 0