Question

I need it to be answered in a detailed form

Answer 1

$\textbf {Hey there, here is the solution.}$

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a1 = -2

d = -5

STEP 1: Find the AP series for nth term:

an = a1 + (n - 1)d

an = -2 + ( n - 1) (-5)

an = -2 -5n + 5

an = -5n + 3

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STEP 2: Find n when term = -77

an = -5n + 3

-77 = -5n + 3

5n = 77 + 3

5n = 80

n = 16

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STEP 3: Find the sum:

Sn = n/2 ( a1 + an)

S16 = 16/2 ( -2 - 77)

S16 = -632

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Answer: The sum of this AP up to the term -77 is -632
.

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⭐$\textbf {Cheers}$⭐