Question

$\huge\underline\mathfrak{Attention!!}$


Find the sum :



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


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Answer 1

$\huge\underline{Solution}$

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Given sequence has two APs

The second number of any number is AP to it.

Let takes 2 APs

First one :

5,9,13,17 upto 81

Here

a=5 , l=81 and d=4

l=a+(n-1)d

81=5+(n-1)4

76=(n-1)4

n-1=19

n=20

Sum of terms = 20/2 (5+81)

=10(86)

=860

Second one:

-41, -39, -37... -5 and -3

Here

a= -41 d=2 and l=-3

l=a+(n-1)d

-3=-41+(n-1)2

38=(n-1)2

n-1=19

n=20

Sum of terms in this case=

20/2 (-41+(-3))

10(-44)

-440

.

.

.

.

Now the total sum of the given sequence=

Sum of first AP and Second AP

=860+(-440)

=420

Answer 2

Answer:

Given sequence has two APs

The second number of any number is AP to it.

Let takes 2 APs

First one :

5,9,13,17 upto 81

Here

a=5 , l=81 and d=4

l=a+(n-1)d

81=5+(n-1)4

76=(n-1)4

n-1=19

n=20

Sum of terms = 20/2 (5+81)

=10(86)

=860

Second one:

-41, -39, -37... -5 and -3

Here

a= -41 d=2 and l=-3

l=a+(n-1)d

-3=-41+(n-1)2

38=(n-1)2

n-1=19

n=20

Sum of terms in this case=

20/2 (-41+(-3))

10(-44)

-440

.

.

.

.

Now the total sum of the given sequence=

Sum of first AP and Second AP

=860+(-440)

=420

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