Question

margaret is writing a recursive function for the geometric sequence: 10, 30, 90, 270, \dots10,30,90,270

Answer 1

$Answer:\ b_n=3^{n-1}b_1$

Step-by-step explanation:

$\displaystyle\\10,\ 30,\ 90,\ 270\\\\b_1=10\\\\b_2=30\\\\b_3=90\\\\b_4=270\\\\q=\frac{b_2}{b_1}=\frac{b_3}{b_2}=\frac{b_4}{b_3} \\\\ q=\frac{30}{10} =\frac{90}{30} =\frac{270}{90} \\\\q=3\\\\Hence,\\\\b_1=10*3^0=10*1=10\\\\b_2*10*3^1=10*3=30\\\\b_3=10*3^2=10*9=90\\\\b_4=10*3^3=10*27=270\\\\Thus,\\b_n=3^{n-1}b_1$