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

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Solution:

Given AP is -6, -11/2, -5…
Here a = –6, d = (–11/2) + 6 = 1/2
Sum of n terms of AP, Sn = – 25
Using sum of n term of AP formula

⇒ n2 – 25n + 100 = 0
⇒ n2 – 20n – 5n + 100 = 0
⇒ n(n – 20) – 5(n – 20) = 0
⇒ (n – 20)(n – 5) = 0
⇒ (n – 20) = 0 or (n – 5) = 0
∴ n = 20 or n = 5

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