For the following sequence determine the common difference (if it is an arithmetic sequence) or the common ratio (if it is a geometric sequence). 8sqrt3,quad24,quad24sqrt3,quad dots (sqrt3)/(3) sqrt3 2sqrt3 (2sqrt3)/(3)

Question

For the following sequence determine the common difference (if it is an arithmetic sequence) or the common ratio (if it is a geometric sequence).  8sqrt3,quad24,quad24sqrt3,quad dots  (sqrt3)/(3)  sqrt3  2sqrt3  (2sqrt3)/(3)

Bytelearn · Accepted Answer

Identify Sequence Type: First, let's identify whether the sequence is arithmetic or geometric. An arithmetic sequence has a common difference between terms, while a geometric sequence has a common ratio. To determine this, we can compare the ratio of consecutive terms. Let's calculate the ratio of the second term to the first term. Ratio = 24 / (8√3)Calculate Ratio: Now, let's simplify the ratio. Ratio = 24 / (8√3) = 3 / √3Simplify Ratio: To further simplify, we can rationalize the denominator. Ratio = (3 / √3) * (√3 / √3) = 3√3 / 3Check Consistency: After simplifying, we get: Ratio = 3√3 / 3 = √3Calculate Next Ratio: Now, let's check if this ratio is consistent with the next pair of terms. We calculate the ratio of the third term to the second term. Ratio = (24√3) / 24Simplify Next Ratio: Simplify the ratio. Ratio = (24√3) / 24 = √3Conclude Geometric Sequence: Since the ratio between consecutive terms is consistent and equal to √3, we can conclude that the sequence is geometric with a common ratio of √3.

Full solution

More problems from Determine end behavior of polynomial and rational functions

Related topics