The sequence 4, 11, 18, 25, 32... (a) Find the nth term formula. (b) Is 200 a term in this sequence? (c) If this sequence represents weekly savings (in rupees), how much is saved after 52 weeks? Then: Explain why a newspaper headline saying 'Average Salary Rises to £50,000' can be misleading.

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Accepted Answer

(a) NTH TERM: Difference between consecutive terms = 7 (arithmetic sequence). First term = 4. nth term = first term + (n−1) × difference = 4 + (n−1) × 7 = 4 + 7n − 7 = 7n − 3. CHECK: n=1: 7(1)−3=4 ✓. n=2: 7(2)−3=11 ✓. n=5: 7(5)−3=32 ✓. (b) IS 200 A TERM? Set 7n−3=200 → 7n=203 → n=29. Since n=29 is a WHOLE POSITIVE NUMBER, YES, 200 is the 29th term. (If n were not a whole number, 200 would NOT be in the sequence.) (c) SAVINGS AFTER 52 WEEKS: 52nd term = 7(52)−3 = 364−3 = 361 rupees (savings in week 52). But the question asks total after 52 weeks. Sum of arithmetic series = n/2 × (first term + last term) = 52/2 × (4 + 361) = 26 × 365 = 9490 rupees total saved after 52 weeks. WHY 'AVERAGE SALARY = £50,000' CAN BE MISLEADING: If the word 'average' means MEAN, then a few very high earners (CEOs, directors earning £500k+) can PULL UP the mean dramatically. Most workers could earn far less than £50,000 while the MEAN is £50,000. Example: 10 employees earning: £20k, £22k, £25k, £28k, £30k, £32k, £35k, £38k, £40k, £230k (CEO). Mean = £500k / 10 = £50k. But 9 out of 10 employees earn LESS than £50k. The MEDIAN would be (30+32)/2 = £31k — a much more accurate reflection of what a 'typical' employee earns. The MEDIAN is the appropriate measure when data is skewed by outliers.

Practice — Algebra, Geometry and Statistical Reasoning — Patterns in Space and Data

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