Determine the first five terms of the geometric sequence.
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A) -7, -10, -13, -16, -19
B) -3, 21, -63, 189, -567
C) -7, 21, -63, 189, -567
D) -7, -21, -63, 189, -567

Question

Determine the first five terms of the geometric sequence.
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A) -7, -10, -13, -16, -19 
B) -3, 21, -63, 189, -567 
C) -7, 21, -63, 189, -567 
D) -7, -21, -63, 189, -567

Quizplus · Accepted Answer

In a geometric sequence, each term is obtained by multiplying the previous term by a constant factor. To find this constant factor, we can divide any term by the previous term. For example,

-7 ÷ 11 = -0.63636… (rounded to 2 decimal places)
21 ÷ (-7) = -3
-63 ÷ 21 = -3
189 ÷ (-63) = -3
-567 ÷ 189 = -3

Therefore, the common ratio of this sequence is -3. To find the first term, we can use the fact that the second term is obtained by multiplying the first term by the common ratio.

-7 × (-3) = 21

So the first five terms are:

-7, 21, -63, 189, -567.

The correct choice is C. In a geometric sequence, each term is obtained by multiplying the previous term by a constant ratio. To find the first five terms, we need to know the first term and the constant ratio. Unfortunately, this information is not provided in the given sequence. However, we can still figure out the answer by using trial and error. Starting with the first term (which could be any number), we multiply it by the same constant ratio to get the second term, and so on. Only option C matches the resulting sequence: -7, 21, -63, 189, -567.

Determine the First Five Terms of the Geometric Sequence