Question

Which of the following is the explicit formula for the nth term of the sequence?

Answer 1

To find:

The explicit formula for the nth term of the sequence.

Solution:

The recursive formula of the sequence is given by:

$a_n=6a_{n-1}$

Here, a1 = 0.75. Find first few terms of the sequence,

$a_1=0.75,a_2=6(0.75)=4.5,a_3=6(4.5)=27,...$

So, the explicit formula that satisfy the given sequence is:

$a_n=0.75\cdot(6)^{n-1}$

Thus, option B is correct.