Sum of the first n terms of an AP sheet3-mark answer frameThe sum of the first 6 terms of an AP is 72 and the sum of the first 10 terms is 200. Find a, d and Sₙ.
How to lay out the answer. Follow the frame, then write it in your own words.
- 1 · Write what is given and what is to be found. Given: S₆ = 72 and S₁₀ = 200. To find: a, d and Sₙ.
- 2 · Write the formula or theorem. Sₙ = n/2 [2a + (n − 1)d]
- 3 · Form two equations.
- S₆ = 3(2a + 5d) = 72, so 2a + 5d = 24 ... (1)
- S₁₀ = 5(2a + 9d) = 200, so 2a + 9d = 40 ... (2)
- 4 · Solve them.
- (2) − (1): 4d = 16, so d = 4
- From (1): 2a = 24 − 20 = 4, so a = 2
- 5 · Find Sₙ. Sₙ = n/2 [4 + (n − 1) × 4] = n/2 × 4n = 2n²
- 6 · Check and box the answer. Check: S₆ = 2 × 36 = 72 and S₁₀ = 2 × 100 = 200. Answer: a = 2, d = 4, Sₙ = 2n².
Scoring tip: Simplify each equation before solving. Dividing 72 by 3 and 200 by 5 first keeps the numbers small.
