Question

The sum if the arithmetic series below is 20882. How many terms must be in this series?

Answer 1

The number of terms in the arithmetic series -13, -9, -5, ...., with the sum of the series being 20882 is 106, making option D the right choice.

The sum of an arithmetic series with the first term a, the common difference d, and the number of terms d, is given as:

S = (n/2)(2a + (n - 1)d).

In the question, we are asked to find the number of terms in the arithmetic series -13, -9, -5, ...., with the sum of the series being 20882.

The first term of the series, a = -13.

The common difference of the series, d = -9 - (-13) = 4.

The sum of the series, S = 20882.

We assume the number of terms to be n.

Putting all the values in the formula for the sum of an arithmetic series, we get:

20882 = (n/2)(2(-13) + (n - 1)4),

or, 41764 = n(4n - 30),

or, 4n² - 30n - 41764 = 0,

or, 2(2n + 197)(n - 106) = 0,

which gives, either n = 106 or, n = -197/2 = -98.5, which is not possible, as n is the number of terms, which cannot be negative.

Thus, n = 106.

Thus, the number of terms in the arithmetic series -13, -9, -5, ...., with the sum of the series being 20882 is 106, making option D the right choice.

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