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

Here, a = -6,

and Sn = -25

We know that,

-100 = n[-25 + n]

n2 – 25n + 100 = 0

n2 – 20n – 5n + 100 = 0

n(n – 20) - 5(n – 20) = 0

(n – 20)(n – 5) = 0

n – 5 = 0 or n – 20 = 0

n = 5 or n = 20

So, n = 5 or 20

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