Hint
The difference is constant. Subtract the known-term equations to find d, then recover a.
Worked solution
(a)
\(\displaystyle a+d=13\) and \(\displaystyle a+4d=16\); subtract to obtain \(\displaystyle 3d=3\), then recover a.
Answer: \(12\) and \(1\)
(b)
There are three common differences from \(\displaystyle u_{2}\) to \(\displaystyle u_{5}\).
\(1\)
Answer: \(1\)
(c)
Use a+(n−1)d.
\(19\)
Answer: \(19\)
Maths4U indicative marking guidance
Maths4U indicative marking guidance, not an official mark scheme. Credit complete valid alternatives and consequential reasoning; an unexplained final answer does not earn a method mark.
(a) · 2 marks
- 1 mark: Form the two equations from the given indexed terms and solve simultaneously.
- 1 mark: Give all results requested in this part, with the correct signs, exact values, units, branch and boundary inclusion where applicable.
Alternative methods: Any complete mathematically valid alternative method with the same restrictions and equivalent exact result is acceptable.
Common error: The first term has index 1, so the multiplier is n−1.
(b) · 2 marks
- 1 mark: There are three common differences from \(\displaystyle u_{2}\) to \(\displaystyle u_{5}\).
- 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: Do not confuse the n-th term with the sum of n terms.
(c) · 2 marks
- 1 mark: Use a+(n−1)d.
- 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: The first term has index 1, so the multiplier is n−1.
Total: 6 marks.