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* a_(n-1)`

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

`a_1=(1)/(3)`

`a_2=(1)/(3)*4^(2-1)=(4)/(3)`

`a_3=(1)/(3)*4^(3-1)=(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* a_(n-1)`

We can test the equation to make sure:

`a_3=4* a_(3-1)=4* a_2=4*(4)/(3)=(16)/(3)`