Arithmetic Sequences: Applications questions from the QCAA externals

Arithmetic sequences form the backbone of simple interest, taxes, and depreciation calculations, among others. This video takes a unique analytical approach by examining Queensland Curriculum and Assessment Authority (QCAA) external exams from the past three years to test these skills. Our first example involves a staircase initially 1.2 meters high. By adding each 0.25-meter stair, an arithmetic sequence emerges: starting from 1.45 meters, increasing by 0.25 meters per step. The arithmetic sequence rule here is the nth term equals the first term (1.45) plus (n-1) times the common difference (0.25). Beware errors when converting to centimeters; in meter terms, the correct answer is C. Next, we move to a 2022 exam problem involving music playlists. Here, T1 represents 87 songs with a common difference of 122 (calculated as 209 minus 87). The 25th week's song count, using the formula Tn = 87 + (n-1) × 122, results in 3,015 songs—a clear application of arithmetic sequences. Finally, tackle a water tank problem: starting with 12,500 liters, losing 153 liters per minute until reaching 5,000 liters. Apply an arithmetic sequence formula to model the situation and determine the time span the tap was left running. Each example highlights real-world applications of arithmetic sequences, reinforcing their educational and practical value. Find 100's more videos linked to the Australia Senior Maths Curriculum at http://mathsvideosaustralia.com/