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## how many terms of AP – 6. – 11 by 2 .minus 5 are needed to be the sum -25

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how many terms of AP – 6. – 11 by 2 .minus 5 are needed to be the sum -25

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Mathematics
3 years
2021-07-24T21:13:48+00:00
2021-07-24T21:13:48+00:00 1 Answers
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## Answers ( )

Given:The terms of a sequence are:

To find:The number of terms whose sum is -25.

Solution:We have, the given sequence:

Here, the first term is -6.

Similarly,

The difference between consecutive terms are same. So, the given sequence is an arithmetic sequence with common difference 0.5.

The sum of n terms of an arithmetic sequence is:

Where, a is the first term, d is the common difference.

Putting , we get

Splitting the middle term, we get

Using zero product property, we get

and

and

and

Therefore, the sum of either 5 or 20 terms is -25.