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How many terms of the A.P. 27, 24, 21, .... should be taken so that their sum is zero? - Mathematics

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How many terms of the A.P. 27, 24, 21, .... should be taken so that their sum is zero?

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Solution

The given AP is 27, 24, 21, ..

First term of the AP = 27

Common difference = 24 − 27 = −3

Let the sum of the first x terms of the AP be 0.

Sum of first x terms = `x/2`[2×27+(x1)(3)]=0

`x/2`[54+(3x+3)]=0

x(543x+3)=0

x(573x)=0

Now, either x = 0 or 57 − 3x = 0.

Since the number of terms cannot be 0, x0.

∴ 57 − 3x = 0

⇒ 57 = 3x

x = 19

Thus, the sum of the first 19 terms of the AP is 0.

Concept: Sum of First n Terms of an AP
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