Hint
Use the stated units and precision. Divide consecutive terms to identify the common multiplier, then count multiplications from index 1.
Worked solution
(a)
The consecutive ratio is 4 and the term at \(\displaystyle n=1\) is 4.
Answer: \(T_n=4\times 4^{n-1}\)
(b)
Divide consecutive terms to identify the common multiplier, then count multiplications from index 1.
\(4\)
Answer: \(4\)
(c)
Divide consecutive terms to identify the common multiplier, then count multiplications from index 1.
\(65536\)
Answer: \(65536\)
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 ratio and use exponent n−1 so the first term is correct.
- 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: Divide consecutive terms to identify the common multiplier, then count multiplications from 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: Check the answer against the original conditions.
(c) · 2 marks
- 1 mark: Divide consecutive terms to identify the common multiplier, then count multiplications from 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.