Hint
State both summation limits. Apply the first-power summation identity.
Worked solution
(a)
\(\displaystyle \frac{n(n+ 1)}{2}= 45\)
Answer: \(45\).
Answer: \(45\)
(b)
\(\displaystyle \frac{n(n+ 1)(2n+ 1)}{6}= 285\)
Answer: \(285\).
Answer: \(285\)
(c)
\(4\sum r^2+7\sum r+n=1464\)
Answer: \(1464\).
Answer: \(1464\)
Maths4U indicative marking guidance
Maths4U indicative marking guidance, not an official mark scheme. Credit valid alternative reasoning and consequential working; do not award a reasoning mark for an unexplained final answer.
(a) · 2 marks
- 1 mark: Apply the first-power summation identity.
- 1 mark: Obtain the stated result with the required sign, units and domain.
Alternative methods: Any complete mathematically valid method with the stated assumptions and equivalent result is acceptable.
Common error: Do not replace \(\displaystyle \Sigma r^{2}\) by \(\displaystyle (\Sigma r)^{2}\).
(b) · 2 marks
- 1 mark: Apply the square summation identity.
- 1 mark: Obtain the stated result with the required sign, units and domain.
Alternative methods: Any complete mathematically valid method with the stated assumptions and equivalent result is acceptable.
Common error: Adjust the number of terms when the sum does not start at one.
(c) · 2 marks
- 1 mark: Separate the polynomial terms before substituting the standard sums.
- 1 mark: Obtain the stated result with the required sign, units and domain.
Alternative methods: Any complete mathematically valid method with the stated assumptions and equivalent result is acceptable.
Common error: Do not replace \(\displaystyle \Sigma r^{2}\) by \(\displaystyle (\Sigma r)^{2}\).
Total: 6 marks.