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

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

#### 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+(x1)(5)]=0

x/2[130+(5x+5)]=0

x(1305x+5)=0

x(1355x)=0

Now, either x = 0 or 135 − 5x = 0.

Since the number of terms cannot be 0, x0.

∴ 135 − 5x = 0

⇒ 135 = 5x

⇒ x = 27

Thus, the sum of the first 27 terms of the AP is 0.

Concept: Sum of First n Terms of an AP
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