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=(10)/(40)=(1)/(4) \\ r=(5)/(8)*(2)/(5)=(10)/(40)=(1)/(4) \\ a_8=40*((1)/(4))^(8-1) \\ a_8=40*((1)/(4))^7 \\ a_8=40*(1)/(16384)_{}^{} \\ a_8=(40)/(16384)=(20)/(8192)=(5)/(2048) \\ a_8=(5)/(2048) \end{gathered}`