Hint
Use the stated units and precision. Compare the supplied powers-of-index pattern, then determine its scale and constant term.
Worked solution
(a)
The second difference is 4, so the scale is 2. The first term determines the additive constant 3.
Answer: \(T_n=2n^{2}+3\)
(b)
Isolating the power gives \(n^{2}=36\). Taking the positive integer root gives \(\displaystyle n=6\).
Answer: \(6\)
(c)
Compare the supplied powers-of-index pattern, then determine its scale and constant term.
\(3\)
Answer: \(3\)
Maths4U indicative marking guidance
Maths4U indicative marking guidance, not an official mark scheme. Credit complete valid alternative methods and consequential reasoning. An unexplained result does not earn a method mark.
(a) · 3 marks
- 1 mark: Use the appropriate finite differences or compare consecutive powers of n.
- 1 mark: Determine the additive adjustment and verify the resulting rule in the supplied terms.
- 1 mark: Give the complete requested result, using the required units, precision and boundary inclusion.
Alternative methods: Any complete mathematically valid alternative method with the same restrictions and equivalent exact result is acceptable.
Common error: Keep intermediate values exact until the final step.
(b) · 2 marks
- 1 mark: Isolate the index power and select a positive integer index that checks in the rule.
- 1 mark: Give the complete requested result, using the required units, precision and boundary inclusion.
Alternative methods: Any complete mathematically valid alternative method with the same restrictions and equivalent exact result is acceptable.
Common error: Check the answer against the original conditions.
(c) · 2 marks
- 1 mark: Compare the supplied powers-of-index pattern, then determine its scale and constant term.
- 1 mark: Give the correct requested result, retaining signs, units and any domain restrictions.
Alternative methods: Any complete mathematically valid alternative method with the same restrictions and equivalent exact result is acceptable.
Common error: Keep intermediate values exact until the final step.
Total: 7 marks.