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3 February, 02:04

Select the correct answer.

What is the sum of this arithmetic series?

586 + 564 + 542 + ... + 212

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Answers (1)
  1. 3 February, 02:20
    0
    sum of the series = 7182

    Step-by-step explanation:

    This is an arithmetic series. The first term is known as 586 and the last term is known as 212. We are ask to find the sum of the series. The common difference of this sequence is - 22. The difference between the next term and the previous term is - 22. Let us find the number of terms.

    common difference = 564 - 586 = - 22

    number of terms = n

    nth term = a + (n - 1) d

    212 = 586 + (n - 1) - 22

    212 = 586 - 22n + 22

    212 - 586 - 22 = - 22n

    -396 = - 22n

    divide both sides by - 22

    n = - 396/-22

    n = 18

    Using the formula for sum

    sum of nth term = n/2 (a + l)

    where

    l = last term

    a = first term

    n = number of term

    sum of nth term = n/2 (a + l)

    sum of nth term = 18/2 (586 + 212)

    sum of nth term = 9 (798)

    sum of the series = 7182
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