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The first three elements of an arithmetic sequence are 20,16, and 12. Which element is...

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spock3 | Student, Undergraduate | (Level 2) Honors

Posted October 10, 2011 at 9:43 PM via web

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The first three elements of an arithmetic sequence are 20,16, and 12. Which element is -96?

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted October 10, 2011 at 10:19 PM (Answer #2)

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The nth term of an arithmetic series is given by Tn = a + (n - 1)d, where a is the first term and d is the common difference.

The first three terms of the series you have given are 20, 16 and 12. The first term of the series is 20, a = 20 and the common difference is 16 - 20 = 12 - 16 = -4

If -96 is the nth term: -96 = 20 - (n - 1)*4

=> n - 1 = (96 + 20)/4 = 29

=> n = 30

The 30th term of the series is -96

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