Geometric sequences can have negative common ratios, creating alternating sequences. Use \(T_n = ar^{n-1}\). Given: a = 3, r = -2, n = 4. Substitution: \(T_4 = 3 \times (-2)^{4-1} = 3 \times (-2)^3\). Calculate: \((-2)^3 = -8\) (negative because odd power). \(T_4 = 3 \times (-8) = -24\). Verification by listing: \(T_1 = 3\), \(T_2 = 3 \times (-2) = -6\), \(T_3 = -6 \times (-2) = 12\), \(T_4 = 12 \times (-2) = -24\) ✓. Notice the pattern: 3, -6, 12, -24, ... (signs alternate). Important: When r is negative, pay attention to whether the power is odd (result negative) or even (result positive). Common mistake: Students sometimes forget the negative sign or miscalculate with negative numbers. In ECZ exams, negative ratio questions test careful arithmetic and understanding that GP principles work regardless of whether r is positive or negative. Take extra care with signs in your working.

Break down complex topics into smaller, manageable chunks for easier recall.

Zambia

• Joseph Soko – 101 pts

• Distance of A Straight Line
• Mid-point of A Line
• Equation of a Straight Line
• Parallel and Perpendicular Lines
• COMMUNICATION SYSTEMS