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Find S20 for the series -1 + -3 + -5 + -7 +...

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emstavro | (Level 3) eNoter

Posted September 17, 2013 at 7:52 PM via web

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Find S20 for the series -1 + -3 + -5 + -7 +...

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jeew-m | College Teacher | (Level 1) Educator Emeritus

Posted September 17, 2013 at 8:08 PM (Answer #1)

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According to the series;

`T_1 = -1`

`T_2 = -3`

`T_3 = -5`

`T_4 = -7`

`T_2-T_1 = -3-(-1) = -2`

`T_3-T_2 = -5-(-3) = -2`

So the terms follows an arithmatic series with a = -1 and d = -2.

Sum of an arithmaic series is given by;

`S_n = n/2(2a+(n-1)d)`

`S_20 = 20/2(2xx(-1)+(20-1)(-1))`

`S_20 = -210`

So the sum of 20 terms in the series is -210.

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