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What is the sum of the first six terms of the geometric series?

2 – 4 + 8 – 16 + ...
Group of answer choices

-42

42

-420

126

What is the sum of the geometric series?

-2, 6, -18, 54
Group of answer choices

-122

54

40

-2

What is the sum of the geometric series?

1, 2, 4, 8, 16, 32, 64, 128, 256
Group of answer choices

-511

-72

-144

511

Step-by-step explanation:

The formula for determining the sum of n terms, Sn of a geometric sequence is expressed as

Sn = (ar^n - 1)/(r - 1)

Where

n represents the number of term in the sequence.

a represents the first term in the sequence.

r represents the common ratio.

1) 2 – 4 + 8 – 16 + ...

a = 2

r = - 4/2 = - 2

n = 6

Since r is negative, we would use

Sn = a(1 - r^n)/(1 - r)

Therefore, the sum of the first 6 terms, S6 is

S6 = 2(1 - (- 2^6))/(1 - - 2)

S6 = 2(1 - 64)/3 = (2 × - 63)/3

S6 = - 42

2) -2, 6, -18, 54

a = - 2

n = 4

r = 6/- 2 = - 3

S4 = - 2(1 - (- 3^4))/(1 - - 3)

S6 = - 2(1 - 81)/4 = (- 2 × - 80)/4

S6 = 40

3) 1, 2, 4, 8, 16, 32, 64, 128, 256

r = 2/1 = 2

n = 9

a = 1

Sn = (ar^n - 1)/(r - 1)

S9 = (1 × 2^9 - 1)/(2 - 1)

S9 = 512 - 1

S9 = 511

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step-by-step explanation:

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