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

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

Posted by Mehul Kedia 4 years, 8 months ago

CBSE > Class 10 > Mathematics

1 answers

Gaurav Seth 4 years, 8 months ago

The series can be written as

(5 + 9 + 13 + .... + 81) + [(- 41) + (- 39) + (- 37) + (- 35) ... (- 5) + (- 3)]

For the series (5 + 9 + 13 + ... + 81)

a = 8

d = 9 - 5 = 5

and a(n) = 81

Then, a(n) = 5 + (n - 1)4 = 81

or, (n - 1)4 = 76

⇒ n = 20

S(n) = 20/2(5 + 81)

= 860

For Series (- 41) + (- 39) + (- 37) + (- 35) ... (- 5) + (- 3)

a(n) = - 3

a = - 41

d = 2

Then, a(n) = - 41 + (n - 1)(2)

⇒ n = 20

Now, S(n) = 20/2[- 41 + (- 3)]

= - 440

Sum of the series = 860 - 440

= 420

Hence, the sum of the following series is 420.

1Thank You

ANSWER

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