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`

Explanation:

`\displaystyle\\10,\ 30,\ 90,\ 270\\\\b_1=10\\\\b_2=30\\\\b_3=90\\\\b_4=270\\\\q=(b_2)/(b_1)=(b_3)/(b_2)=(b_4)/(b_3) \\\\ q=(30)/(10) =(90)/(30) =(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`