The first term of a linear sequence is 7.5 and the fourth term is 3.find the number of terms in the sequence if its sum is -9.

Answer 1

use your definitions.

a = 7.5
a+ 3d = 3
7.5 + 3d = 3
d = -1.5

sum(n) = (n/2)(2a + (n-1)d)
-9 = (n/2)(15 + (n-1)(-1.5) )
-18 = n(15 - 1.5n + 1.5)
-18 = 16.5n - 1.5n^2
double and re-arrange
3n^2 - 33n - 36 = 0
n^2 - 11n - 12 = 0
(n+1)(n-12) = 0
n = -1 or n = 12

there are 12 terms