June 2016 Paper 1 Q3
3 The \(n\)th term of a sequence is \(\quad \dfrac{3n}{5n + 12}\)
(a) Work out the position of the term that has a value of \(\dfrac{1}{2}\) [2 marks]
(b) Write down the limiting value of \(\quad \dfrac{3n}{5n + 12} \quad\) as \(n \to \infty\) [1 mark]
| Answer | Mark | Comments |
|---|---|---|
| \(2(3n) = 5n + 12\) or \(3n = \dfrac{5n + 12}{2}\) or \(3n = \dfrac{1}{2}(5n + 12)\) or \(3n = 2.5n + 6\) or \(0.5n = 6\) | M1 | oe |
| 12 | A1 | Accept 12th term |
Additional guidance
Do not accept an embedded answer, they must state 12
Trial and improvement is 2 if correct, otherwise 0
\(\dfrac{3n}{5n + 12} = \dfrac{1}{2}\) is M0
| Answer | Mark | Comments |
|---|---|---|
| \(\dfrac{3}{5}\) or 0.6 | B1 |