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प्रश्न
How many terms of the A.P. 65, 60, 55, .... be taken so that their sum is zero?
उत्तर
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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