Question

Hello. Im trying to help my 9th grade autistic daughter with her test corrections for extra credit and so she fully understands the questions she missed. Its been over 20 yrs since I had Algebra 1 so my Algebra skills are very rusty. She easily gets frustrated and impatient so Im trying to do some leg work before sitting down with her to do it. I appreciate your assistance with this.

Answer 1

ANSWER:

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

STEP-BY-STEP EXPLANATION:

We have the following sequence:

$a_n=\frac{1}{3}\mleft(4\mright)^{n-1}$

The initial term is when n equals 1, so we replace:

$\begin{gathered} a_1=\frac{1}{3}\mleft(4\mright)^{1-1}=\frac{1}{3}\cdot4^0=\frac{1}{3}\cdot1=\frac{1}{3} \\ a_1=\frac{1}{3} \end{gathered}$

The initial term is 1/3