Determine the first five terms of the geometric sequence.
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A) 3, 7, 11, 15, 19
B) 3, 12, 48, 192, 768
C) 4, 12, 36, 108, 324
D) 12, 48, 192, 768, 3072

Question

Determine the first five terms of the geometric sequence.
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A) 3, 7, 11, 15, 19 
B) 3, 12, 48, 192, 768 
C) 4, 12, 36, 108, 324 
D) 12, 48, 192, 768, 3072

Quizplus · Accepted Answer

The sequence is most likely of the form: a, ar, ar^2, ar^3, ar^4 with an unknown value for a and r. Looking at the options, option B best fits this form with a=3 and r=4. The terms of this sequence are 3, 12, 48, 192, 768. The sequence is most likely a geometric sequence since it has a long alphanumeric string as its identifier. To find the common ratio, we divide each term by the preceding term.

12/3 = 4

48/12=4

192/48=4

768/192=4

3072/768=4

We have a common ratio of 4. Then, starting with the first term 3, we can generate the first five terms by multiplying by 4 successively:

3, 12, 48, 192, 768

Determine the First Five Terms of the Geometric Sequence