Question

Find A.P. whose sum of first 11 term is zero

Answer 1

Answer:

Any series, which consists of 5 positive terms with a common difference, the same set of terms with a negative sign, and zero as the middle term.

Step-by-step explanation:

In an AP, the average of the series is its middle term.

Here, Average= (0/15)=0, which is the middle term.

A sample AP: -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5

Another sample AP: -15, -12, -9, -6, -3, 0, 3, 6, 9, 12, 15

Answer 2

The AP of 11 term is -10, -8, -6, -4, -2, 0, 2, 4, 6, 8, 10

Step-by-step explanation:

Let the AP of 11 term be

a-5d, a-4d, a-3d, a-2d, a-d, a, a+d, a+2d, a+3d, a+4d, a+5d

Sum of 11 term of AP is 0

a-5d + a-4d + a-3d + a-2d + a-d + a + a+d + a+2d + a+3d + a+4d + a+5d = 0

11a = 0

  a = 0

In the series a is 6th term

It will symmetry both sides.

So, the value of d would be any real number

Let d = 2

then AP will be,

-10, -8, -6, -4, -2, 0, 2, 4, 6, 8, 10

If we change the value of d AP will be change.

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