Multiple Choice
Find the common ratio for the geometric sequence.
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15. Sequences, Series, and the Binomial Theorem
Geometric Sequences
Multiple Choice
Write the first four terms of the following geometric sequence.
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Verified step by step guidance1
Identify the first term \(a_1\) and the common ratio \(r\) of the geometric sequence. Here, \(a_1 = \frac{3}{4}\) and \(r = \frac{2}{3}\).
Recall that the \(n\)th term of a geometric sequence is given by the formula: \(a_n = a_1 \times r^{n-1}\).
Calculate the second term \(a_2\) by substituting \(n=2\) into the formula: \(a_2 = a_1 \times r^{2-1} = a_1 \times r\).
Calculate the third term \(a_3\) by substituting \(n=3\): \(a_3 = a_1 \times r^{3-1} = a_1 \times r^2\).
Calculate the fourth term \(a_4\) by substituting \(n=4\): \(a_4 = a_1 \times r^{4-1} = a_1 \times r^3\).
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