Questions: Find the 11th term of the geometric sequence. -18,36,-72, ...

Solution Steps

To find the 11th term of a geometric sequence, we need to identify the first term (a) and the common ratio (r). The nth term of a geometric sequence can be found using the formula: \[ a_n = a \cdot r^{(n-1)} \] Here, the first term \( a = -18 \) and the common ratio \( r = \frac{36}{-18} = -2 \). We need to find the 11th term (\( n = 11 \)).

The first term of the geometric sequence is given as \( a = -18 \). The common ratio \( r \) can be calculated as: \[ r = \frac{36}{-18} = -2 \]

The formula for the \( n \)-th term of a geometric sequence is: \[ a_n = a \cdot r^{(n-1)} \] Here, \( n = 11 \).

Substitute \( a = -18 \), \( r = -2 \), and \( n = 11 \) into the formula: \[ a_{11} = -18 \cdot (-2)^{(11-1)} \]

\[ a_{11} = -18 \cdot (-2)^{10} \] \[ (-2)^{10} = 1024 \] \[ a_{11} = -18 \cdot 1024 = -18432 \]

Final Answer