## Thinking Mathematically (6th Edition)

General Term Formula: $a_n = 1.5 \cdot (-2)^{n-1}$ $a_7=96$
RECALL: The formula for the general term (nth term) of a geometric sequence is: $a_n=a_1 \cdot r^{n-1}$ where r = common ratio $a_1$ = first term $a_n$ = nth term $n$= term number To find the formula for the general term of the given geometric sequence, perform the following steps: (1) Solve/find the values of $a_1$ and $r$ The given sequence has: $a_1 = 1.5$ $r = \frac{-3}{1.5} =-2$ (2) Substitute the values of $a_1$ and $r$ in the formula above. Substituting gives us: $a_n = 1.5 \cdot (-2)^{n-1}$ Therefore, the 7th term of the sequence is: $a_{7}=1.5 \cdot (-2)^{7-1} \\a_{7}=1.5 \cdot (-2)^6 \\a^{7} = 1.5 \cdot 64 \\a_{7} = 96$