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

First term a = -6

Second term = -11/2

Let d be the common difference.

d = Second term – First term

d = -11/2 – (-6) = 6 – 11/2 = 1/2

Sn = Sum of n terms of AP = -25

n2 – 25n + 100 = 0

n2 – 20n – 5n + 100 = 0

n × (n – 20) – 5 × (n – 20) = 0

(n – 20) × (n – 5) = 0

n = 20 or 5

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