Higher January 2022 Paper 1R Q16
16 An arithmetic series has first term 1 and common difference 4
Find the sum of all terms of the series from the 41st term to the 100th term inclusive.
(4)
| Scheme | Marks |
|---|---|
\(\dfrac{100}{2}\left[2 \times 1 + (100 - 1) \times 4\right](= 19\,900)\) oe or \(1 + (41 - 1) \times 4\ (= 161)\) oe or \(1 + (100 - 1) \times 4\ (= 397)\) oe | M1 |
\(\dfrac{40}{2}(2 \times 1 + (40 - 1) \times 4)(= 3160)\) oe or \(\dfrac{41}{2}(2 \times 1 + (41 - 1) \times 4)(= 3321)\) oe or 100 – 41 + 1 (= 60) oe | M1 |
“19 900” – “3160” or \(\dfrac{\text{``}{60}\text{''}}{2}\left[\text{``}{161}\text{''} + \text{``}{397}\text{''}\right]\) or \(\dfrac{\text{``}{60}\text{''}}{2}\left[2 \times \text{``}{161}\text{''} + (\text{``}{60}\text{''} - 1) \times 4\right]\) oe | M1 |
| 16 740 | A1 |
| (4) | |
| (4 marks) |
Notes
M1: for method to find the sum of the first 100 terms
or
for finding the 41st term
or
for finding the 100th term
M1: for method to find the sum of the first 40 terms or 41 terms
or
for finding the number of terms from the 41st term to the 100th term
M1: for finding the difference
or
for finding the sum from the 41st term to the 100th term