Question

In an arithmetic sequence, the nth term a, is given by the formula a, a, + (n-1)d, where a, is the first term and d is the common difference. Similarly, in a geometricsequence, the nth term is given by an = a -1, where r is the common ratio. Use these formulas to determinethe indicated term in the given sequence.5 5The 8th term of 40, 10, 2ag =(Type an integer or a simplified fraction.)2or

Answer 1

The sequence is a geometric progression. Therefore,

$\begin{gathered} a_n=ar^{n-1} \\ r=\frac{10}{40}=\frac{1}{4} \\ r=\frac{5}{8}\times\frac{2}{5}=\frac{10}{40}=\frac{1}{4} \\ a_8=40\times(\frac{1}{4})^{8-1} \\ a_8=40\times(\frac{1}{4})^7 \\ a_8=40\times\frac{1}{16384}_{}^{} \\ a_8=\frac{40}{16384}=\frac{20}{8192}=\frac{5}{2048} \\ a_8=\frac{5}{2048} \end{gathered}$