Select the formula for the n^th term of the sequence. 9,45,225,ldots Show your work here 9+5(n) 9(5)^n-1 9+5(n-1) 9(5)^n None of the above

To find the formula for the $n^{th}$ term of the sequence $9, 45, 225, \ldots$, we need to identify the pattern in the sequence.<br /><br />Let's denote the $n^{th}$ term of the sequence as $a_n$.<br /><br />We can observe that each term in the sequence is obtained by multiplying the previous term by 5.<br /><br />So, we can write the recursive formula for the sequence as:<br />$a_n = 5 \cdot a_{n-1}$<br /><br />Now, let's find the explicit formula for the $n^{th}$ term.<br /><br />We can start by finding the first few terms of the sequence using the recursive formula:<br />$a_1 = 9$<br />$a_2 = 5 \cdot a_1 = 5 \cdot 9 = 45$<br />$a_3 = 5 \cdot a_2 = 5 \cdot 45 = 225$<br /><br />From the above calculations, we can see that each term is obtained by multiplying 9 by 5 raised to the power of $n-1$.<br /><br />Therefore, the formula for the $n^{th}$ term of the sequence is:<br />$a_n = 9 \cdot 5^{n-1}$<br /><br />So, the correct answer is:<br />$9(5)^{n-1}$