Question

(-100)+(-92)+(-84)+ ... +92, Find the sum of the given equation.

Answer 1

a = - 100

d = 8

L = 92

=> 92 = a + (n-1) d

=> 92 = - 100 + (n-1) (8)

=> 192 = (n-1) (8)

=> n - 1 = 24

=> n = 25

Now,

Required sum = n/2 ( a + L)

= 25 /2 ( - 100 + 92)

= 25 × (-8) /2

= 25 × (-4)

= - 100

Answer 2

Hope u like my process
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The given sum is of Arithmetic Progression.
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✔️ Formula to be used :-
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=>
$= > \bf \: sum = \frac{n}{2} (a + l) \\ \\ ( \bf \: where \: \: a = 1st \: \: term \: ..l = last \: \: term) \\ \\ \\ = > nth \: \: term = \bf \: a + (n - 1)d \\ \\ (where \: \bf d \: = \: difference)$

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Given :-
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=> a = $\bf \: - 100 \: \:$

=> d = $\bf \: 8\: \:$

So,

$= > \bf \: a + (n - 1)d = 92 \\ \\ or. \: \: - 100 + (n - 1)8 = 92 \\ \\ or. \: \: (n - 1)8 = 92 + 100 \\ \\ or. \: \: n - 1 = \frac{192}{8} = 24 \\ \\ or. \bf \: \: \: n = 24 + 1 = 25$
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$= > \bf \: sum = \frac{n}{2} (a + l) = \frac{25}{2} ( - 100 + 92) \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \bf = \frac{25}{2} \times- 8 = - 100$
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So

The required sum = $\bf \: - 100 \: \:$
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Hope this is ur required answer

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