# A geometric sequence is defined recursively by an = 4an-1. The 10th term of the sequence is a10 = 3.5. What is a13?

Jul 9, 2015

Using (I think) a different interpretation of the question than Spandy's answer (which I'm not certain I understand):
$\textcolor{w h i t e}{\text{XXXX}}$${a}_{13} = 224$

#### Explanation:

Assuming the "givens" are:
$\textcolor{w h i t e}{\text{XXXX}}$${a}_{n} = 4 {a}_{n - 1}$
$\textcolor{w h i t e}{\text{XXXX}}$${a}_{10} = 3.5$

${a}_{11} = 4 \cdot {a}_{10} = 4 \cdot 3.5 = 14$

${a}_{12} = 4 \cdot {a}_{11} = 4 \cdot 14 = 56$

${a}_{13} = 4 \cdot {a}_{12} = 4 \cdot 56 = 224$