Find the 10th term of the geometric sequence. 7,-21,63,ldots Show your work here Enter your answer

To find the 10th term of the geometric sequence, we first need to determine the common ratio (r) of the sequence. We can do this by dividing any term by its preceding term.<br /><br />Let's use the second term (-21) and the first term (7) to find the common ratio:<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 />\[ a_n = a_1 \cdot r^{(n-1)} \]<br /><br />Where:<br />- \( a_n \) is the nth term<br />- \( a_1 \) is the first term<br />- \( r \) is the common ratio<br />- \( n \) is the term number<br /><br />For the 10th term (\( a_{10} \)):<br />\[ a_{10} = 7 \cdot (-3)^{(10-1)} \]<br />\[ a_{10} = 7 \cdot (-3)^9 \]<br /><br />Now, calculate \((-3)^9\):<br />\[ (-3)^9 = -19683 \]<br /><br />Finally, multiply this by the first term (7):<br />\[ a_{10} = 7 \cdot -19683 \]<br />\[ a_{10} = -137781 \]<br /><br />So, the 10th term of the geometric sequence is:<br />\[ \boxed{-137781} \]