Question

PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!!

The explicit rule for a sequence is given.

Answer 1

Answer:
`a_1=3,\quad a_n=\bigg((1)/(6)\bigg)a_(n-1)`

Explanation:

`\text{The explicit rule is in the format:}\ a_n=a_1(r)^(n-1)\\\text{where}\ a_1\ \text{is the first term, r is the common ratio, and n is the term}`

`\text{So,}\ a_n=3\bigg((1)/(6)\bigg)^(n-1)\ \text{means that}\ a_1=3\ \text{and r}=(1)/(6)`

`\text{The recursive rule applies when given the previous term.}\\ \text{The recursive formula is:}\ a_n=r\cdot a_(n-1)\quad \text{where}\ a_(n-1)\ \text{is the previous term}`

`\text{So, inserting the r-value from the explicit formula into the recursive}\\\text{formula, we get:}\ a_n=\bigg((1)/(6)\bigg)a_(n-1)`