find the sum of 5+(-41)+9+(-39)+13+(-37)+17+.....+(-5)+81+(-3)

1.	find the sum of 5+(-41)+9+(-39)+13+(-37)+17+.....+(-5)+81+(-3)
Answer» The series can be written as(5 + 9 + 13 + .... + 81) + [(- 41) + (- 39) + (- 37) + (- 35) ... (- 5) + (- 3)]For the series (5 + 9 + 13 + ... + 81)a = 8d = 9 - 5 = 5and a(n) = 81Then, a(n) = 5 + (n - 1)4 = 81or, (n - 1)4 = 76⇒\xa0n = 20S(n) = 20/2(5 + 81)=\xa0860For Series (- 41) + (- 39) + (- 37) + (- 35) ... (- 5) + (- 3)a(n) = - 3a = - 41d = 2Then, a(n) = - 41 + (n - 1)(2)⇒\xa0n = 20Now, S(n) = 20/2[- 41 + (- 3)]= - 440Sum of the series = 860 - 440=\xa0420Hence, the sum of the following series is 420.

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