Question

Hello. Im trying to help my 9th grade daughter who is autistic with her math test corrections. It has been over 20 yrs since I had Algebra 1 and Im definitely rusty. She easily gets frustrated and impatient and so Im trying to do some leg work on it before going over it with her. I need help with the second part of this question. Thanks in advance

Answer 1

The recursive formula for a geometric sequence is:

$a_n=r\times a_{n-1}$

We have to find 'r'. This can be done by looking at the terms:

$a_1=\frac{1}{3}$

$a_2=\frac{1}{3}\times4^{2-1}=\frac{4}{3}$

$a_3=\frac{1}{3}\times4^{3-1}=\frac{16}{3}$

The reason 'r' is 4. Each term of the sequence is being multiplicated by 4. Then, the recursive formula will be:

$a_n=4\times a_{n-1}$

We can test the equation to make sure:

$a_3=4\times a_{3-1}=4\times a_2=4\times\frac{4}{3}=\frac{16}{3}$