Select the formula for the n^th term of the sequence. 5,15,45,ldots Show your work here 5(3)^n-1 5+3(n) 5+3(n-1) 5(3)^n None of the above

To find the formula for the $n^{th}$ term of the sequence $5,15,45,\ldots$, we need to identify the pattern in the sequence.<br /><br />Let's examine the given terms:<br />- The first term is 5.<br />- The second term is 15.<br />- The third term is 45.<br /><br />We can observe that each term is obtained by multiplying the previous term by 3. This indicates that the sequence is a geometric sequence with a common ratio of 3.<br /><br />The general formula for the $n^{th}$ term of a geometric sequence is given by:<br />$a_n = a_1 \cdot r^{n-1}$<br /><br />Where:<br />- $a_n$ is the $n^{th}$ term<br />- $a_1$ is the first term<br />- $r$ is the common ratio<br /><br />In this case, the first term $a_1$ is 5 and the common ratio $r$ is 3. Substituting these values into the formula, we get:<br />$a_n = 5 \cdot 3^{n-1}$<br /><br />Therefore, the formula for the $n^{th}$ term of the sequence $5,15,45,\ldots$ is $5(3)^{n-1}$.<br /><br />So, the correct answer is:<br />$5(3)^{n-1}$