Q23 of 176 Page 8

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

Here, a = -6,

and S_n = -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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