Determine the first five terms of the geometric sequence.
-
A) 6, 30, 150, -750, 3750
B) -5, -30, 150, -750, 3750
C) 6, 1, -4, -9, -14
D) 6, -30, 150, -750, 3750

Question

Determine the first five terms of the geometric sequence.
-
A) 6, 30, 150, -750, 3750 
B) -5, -30, 150, -750, 3750 
C) 6, 1, -4, -9, -14 
D) 6, -30, 150, -750, 3750

Quizplus · Accepted Answer

The first term of the sequence is unknown, but we can find it by dividing the second term by the common ratio. To do this, we can use any pair of consecutive terms in the sequence. Let's use the first two terms:

- (-30) ÷ 5 = -6

So the first term is -6. Now we can use this information to find the first five terms of the sequence:

- Term 1: -6
- Term 2: -6 × 5 = -30
- Term 3: -30 × 5 = -150
- Term 4: -150 × 5 = 750
- Term 5: 750 × 5 = 3750

Therefore, the first five terms of the sequence are -6, -30, -150, -750, 3750, and the best choice is D. The first term of the sequence is not given, so we cannot determine it. However, we can find the common ratio by dividing any term by the previous term. 
$-30/6 = -5, 150/-30 = -5, -750/150 = -5, 3750/-750 = -5$
Thus, the common ratio is -5. 
Starting with the first answer choice, we see that the first term is 6 and the common ratio is -5. However, the second term should be $6\cdot(-5)=-30$, not 30. 
Similarly, the third and fourth terms in choice A are incorrect, so we can eliminate it. 
Choice B has the correct common ratio, but the first term should be -5, not 6. 
Choice C does not have a common ratio of -5, so we can eliminate it. 
Therefore, the best choice is D, which has the correct common ratio and an unknown first term.

Determine the First Five Terms of the Geometric Sequence