Question

Find the sum of the series

5+(-41)+9+(-39)+13+(-37)+17+.......+(-5)+81+(-3

Answer 1

Answer:

Step-by-step explanation:

let there be two series in the given series

first 5+9+13........ 81

and the second be -41 + (-39) + (-37)................. -3

number of terms in first series

an=a + (n-1)d

81=5+(n-1)d

76=(n-1)4

19=n-1

n=20

similarly in second series there are 20 terms

now,sum of the two series

sum of given series = sum of first series + sum of second series

= n/2{ 2a +(n-1)d} +n/2{ 2a +(n-1)d}

=n/2[{2*5+19*4} +{2* -41 +19*2}]

=10[{10+76}+{-82+32}]

=10*[86-44]

=10*42

=420

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