Higher June 2022 Paper 3 Q7
7 A is an arithmetic progression.
Here are the first four terms.
13 16 19 22
G is a geometric progression.
Here are the first four terms.
2 4 8 16
\(n\)th term of A = 8th term of G
Work out the value of \(n\). [4 marks]
| Answer | Mark | Comments |
|---|---|---|
| (8th term =) \(2^8\) or 256 | M1 | oe may be implied |
| Common difference of A indicated as 3 | M1 | may be implied eg \(3n \ldots\) or \(\ldots + 3(n - 1)\) |
| \(3n + 10 =\) their 256 or (their \(256 - 10) \div 3\) or (their \(256 - 13) \div 3\) or 81 | M1dep | oe equation eg \(13 + 3(n - 1) = 2^8\) dep on 2nd M1 their 256 may be any number and may be in index form |
| 82 | A1 |
Additional guidance
| \(n + 3\) implies 2nd M1 | |
| Do not award M1 for 256 if it is in a list of powers of 2 unless it is indicated or it is the highest power evaluated | |
| Common difference of 3 may be shown on the progression for the 2nd M1 | |
| 10, (13, 16, 19, 22), 25 without common difference of 3 shown does not imply 2nd M1 | |
| 82 from trial and improvement | M3A1 |
| Embedded answer \(3 \times 82 + 10 = 256\) | M3A0 |
| \(3n + 10 = 256\) or \(3n + 10 = 2^8\) or \(3n = 246\) | M1M1M1 |
| \(3n - 10 = 256\) | M1M1M0 |
| \(3n + 10 = 16\) (\(2^8\) not seen) | M0M1M1 |
| \(3n + 6 = 2^8\) | M1M1M0 |
| \(256 - 22 = 234,\ 234 \div 3\) (indicating common difference of 3) | M1M1M0 |
| \(3n - 8 = 128\) (\(2^8\) not seen) | M0M1M0 |