Question

Given { t, f, 7r, 3n, 9n,...}:

(a) Find the 12th term.

(b) Find the sum of the first 12 terms.

Answer 1

(a)

$$b_4=3n, b_5=9n,...$$

$q=3$

$$b_{12}=3^{12-3}n=19683n$$

The 12th term is $19683n.$

(b)

$$b_4+b_5+...+b_{12}=3n\cdot\dfrac{1-3^9}{1-3}=29523n$$

The sum of the first 12 terms is

$$S_{12}=t+f+7r+29523n$$