A geometric sequence is defined by the equation an = (2)5 − 2n.
Part A: What are the first three terms of the sequence?
Part B: What is the value of r?
Part C: What is the value of a10?
+26379 geometric sequence
\(a_n=2^{5-2n} \)
\( \begin{array}{lcl} n=1: \qquad a_1 = 2^{5-2\cdot 1} =2^{3}=8\\ n=2: \qquad a_2 =2^{5-2\cdot 2} =2^{5-4}=2^1=2\\ n=3: \qquad a_3 = 2^{5-2\cdot 3}=2^{5-6}=2^{-1}=\frac12\\ \hline \\ r = \frac{a_3}{a_2}=\frac{\frac12}{2}=\frac14\\ r = \frac{a_2}{a_1}=\frac{2}{8}=\frac{1}{4}\\ \hline \\ n=10: \qquad a_{10}=2^{5-2\cdot 10}=2^{5-20}=2^{-15}=\frac{1}{2^1} \end{array}\)
