A geometric sequence is given by the recursive rule $a_1=\frac{2}{3},\ a_n=3a_{n-1}$ . Give an explicit rule for the nth term of the sequence $b_1,\ b_2,\ b_3,\ \dots\ ,$ given that $b_1=a_1,\ b_2=a_3,\ b_3=a_5,\ \dots$ .

Step-by-step explanation:

Given

Required

An explicit rule for

Where

We have:

Calculate a2

Calculate a3

Calculate a4

Calculate a5

So:

The above sequence form a geometric sequence.

Calculate common ratio (r)

So, the explicit formula is:

, so:

, so:

Split:

The explicit rule is:

the 4th choice is the correct one

step-by-step explanation: