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

Question

Philoid · Accepted Answer

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

S_n = 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

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