# How many terms of the A.P. –6, -11/2, -5, ….. are needed to give the sum –25?

a= -6, d = (-11/2) + 6 = (-11 + 12)/2 = ½, Sn = -25

-25 = (n/2)[2(-6) + (n -1)(1/2)]

-25 4 = n(-24 + n –1)

- 100 = n(-25 + n)

n2 -25n + 100 = 0

n2 -20n – 5n + 100 = 0

n(n – 20) – 5(n – 20) = 0

(n – 5)(n – 20) = 0

n = 5, n = 20

Therefore the required number of terms is 5 or 20.

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