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Question
How many terms of the A.P. 65, 60, 55, .... be taken so that their sum is zero?
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Solution
The given AP is 65, 60, 55, ...
First term of the AP = 65
Common difference = 60 − 65 = −5
Let the sum of the first x terms of the AP be 0.
Sum of first x terms =`x/2`[2×65+(x−1)(−5)]=0
⇒`x/2`[130+(−5x+5)]=0
⇒x(130−5x+5)=0
⇒x(135−5x)=0
Now, either x = 0 or 135 − 5x = 0.
Since the number of terms cannot be 0, x≠0.
∴ 135 − 5x = 0
⇒ 135 = 5x
⇒ x = 27
Thus, the sum of the first 27 terms of the AP is 0.
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