When you know the first term, last term, and number of terms, use the simpler sum formula: \(S_n = \frac{n}{2}(a + l)\), where l is the last term. This formula is derived from the average of first and last terms multiplied by the number of terms. Given: a = 12, l = 60, n = 9. Substitution: \(S_9 = \frac{9}{2}(12 + 60)\). Calculation: \(S_9 = \frac{9}{2}(72) = \frac{9 \times 72}{2} = \frac{648}{2} = 324\). The sum is 324. Understanding: This formula works because in an arithmetic sequence, terms are evenly distributed. The average term is \(\frac{a + l}{2}\), and multiplying by n gives the total sum. This is analogous to finding the area of a trapezoid (which the sum formula geometrically represents). In ECZ exams, using this formula when appropriate saves time and reduces calculation errors. However, you must know both formulas because sometimes the last term isn't directly given and must be calculated first using \(T_n = a + (n-1)d\).

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• ivwananji siwale – 29 pts

• Mid-point of A Line
• Equation of a Straight Line
• Parallel and Perpendicular Lines
• Area of Rectilinear Figures
• Distance of A Straight Line