Hint
Use the stated units and precision. Use the constant difference and remember that the first term has index 1.
Worked solution
(a)
The common difference is 5. Therefore \(T_n=9+(n-1)5\) = \(5 n + 4\).
Answer: \(T_n=5 n + 4\)
(b)
Substitute the stated positive integer index into the nth-term formula.
Answer: \(44\)
(c)
Use the constant difference and remember that the first term has index 1.
\(5\)
Answer: \(5\)
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) · 2 marks
- 1 mark: Identify the constant first difference and adjust the index so \(\displaystyle n=1\) gives the first term.
- 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: Evaluate the complete nth-term rule at the requested index.
- 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: Use the constant difference and remember that the first term has index 1.
- 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: 6 marks.