What is the $7$th term of the geometric sequence $2, -6, 18, -54, \ldots$?

Identify the common ratio: $r = \dfrac{-6}{2} = -3$. Verify: $\dfrac{18}{-6} = -3$ ✓, $\dfrac{-54}{18} = -3$ ✓. $a_{n} = a_{1} \cdot r^{n - 1}$: $a_{7} = 2 \cdot (-3)^{6} = 2 \cdot 729 = 1{,}458$. Note: $(-3)^{6}$ is **positive** because 6 is even. The signs in the sequence alternate: $+, -, +, -, +, -, +$, so the 7th term is positive. - Trap A ($-2187 = -3^{7}$) uses the wrong exponent. - Traps B and C flip signs or omit factors.