Foundation November 2017 Paper 3 Q18
18 Here is a sequence of patterns made with counters.
(a) Find an expression, in terms of \(n\), for the number of counters in pattern number \(n\). (2)
Bayo has 90 counters.
(b) Can Bayo make a pattern in this sequence using all 90 of his counters?
You must show how you get your answer. (2)
You must show how you get your answer. (2)
| Answer | Mark | Notes |
|---|---|---|
| \(3n + 1\) | M1 | for a method to deduce the \(n\)th term, eg. \(3n + k\), where \(k\) is an integer or \(k\) is omitted or for \(n = 3n + 1\) |
| A1 | for \(3n + 1\) oe (accept \(n\) replaced by another letter) |
| Answer | Mark | Notes |
|---|---|---|
| No (supported) | C1 | for using (their expression in (a)) = 90 or shows that 88 or 91 is in the sequence |
| C1 | for an answer of “No” and a convincing argument eg. pattern number 30 has 91 counters or \((90 - 1) \div 3\ (= 29.66\ldots)\) or shows that the next term after 88 is 91 Note: no ft from (a) |