Find the 8th term of the geometric sequence. -7,-21,-63,ldots Show your work here Enter your answer

To find the 8th term of the geometric sequence $-7,-21,-63,\ldots$, we first need to determine the common ratio of the sequence.<br /><br />The common ratio (r) can be found by dividing any term in the sequence by the previous term. Let's use the second term (-21) and the first term (-7) to find the common ratio:<br /><br />$r = \frac{-21}{-7} = 3$<br /><br />Now that we have the common ratio, we can use the formula for the nth term of a geometric sequence:<br /><br />$a_n = a_1 \cdot r^{(n-1)}$<br /><br />where $a_n$ is the nth term, $a_1$ is the first term, and n is the term number.<br /><br />In this case, $a_1 = -7$, $r = 3$, and $n = 8$. Plugging these values into the formula, we get:<br /><br />$a_8 = -7 \cdot 3^{(8-1)}$<br /><br />$a_8 = -7 \cdot 3^7$<br /><br />$a_8 = -7 \cdot 2187$<br /><br />$a_8 = -15309$<br /><br />Therefore, the 8th term of the geometric sequence $-7,-21,-63,\ldots$ is $-15309$.