Higher November 2022 Paper 1 Q23
23 Here are the first five terms of a geometric sequence.
\(\sqrt{5} \qquad 10 \qquad 20\sqrt{5} \qquad 200 \qquad 400\sqrt{5}\)
(a) Work out the next term of the sequence. (2)
The 4th term of a different geometric sequence is \(\dfrac{5\sqrt{2}}{4}\)
The 6th term of this sequence is \(\dfrac{5\sqrt{2}}{8}\)
Given that the terms of this sequence are all positive,
(b) work out the first term of this sequence.
You must show all your working. (3)
You must show all your working. (3)
| Answer | Mark | Mark scheme |
|---|---|---|
| 4000 | P1 | for process to identify the common ratio, eg \(400\sqrt{5} \div 200\ (= 2\sqrt{5})\) or \(200 \div 400\sqrt{5}\ \left(= \dfrac{1}{2\sqrt{5}}\right)\) or for a process to find the next term of the sequence, eg \(200 \times (200 \div 10)\) |
| A1 | cao |
Additional guidance
May use any 2 consecutive terms
| Answer | Mark | Mark scheme |
|---|---|---|
| 5 | P1 | for process to find the ratio of the 4th and 6th terms, eg \(\dfrac{5\sqrt{2}}{8} \div \dfrac{5\sqrt{2}}{4}\ \left(= \dfrac{1}{2}\right)\) or \(\dfrac{5\sqrt{2}}{4} \div \dfrac{5\sqrt{2}}{8}\ (= 2)\) or for finding that the 2nd term is \(\dfrac{5\sqrt{2}}{2}\) |
| P1 | for complete process to find 1st term, eg \(\dfrac{5\sqrt{2}}{4} \div \left(\dfrac{1}{\sqrt{2}}\right)^3\) | |
| A1 | cao |
Additional guidance
Award 0 marks for a correct answer with no supportive working