Foundation June 2022 Paper 1 Q13
13
(a) The term-to-term rule for a sequence is
| multiply by 2 |
The 3rd term of the sequence is 46
Work out the 1st term.
Give your answer as a decimal. [3 marks]
(b) The term-to-term rule for a different sequence is
| subtract \(k\) |
The 1st term is 34
The 4th term is 10
Work out the value of \(k\). [3 marks]
| Answer | Mark | Comments |
|---|---|---|
| \(46 \div 2\) or 23 or \(4x = 46\) | M1 | oe |
| their \(23 \div 2\) or \(46 \div 2 \div 2\) or \(46 \div 4\) | M1dep | oe may be seen as a fraction eg \(\dfrac{23}{2}\) or \(11\dfrac{1}{2}\) or \(\dfrac{46}{4}\) or \(11\dfrac{2}{4}\) |
| 11.5 | A1 | SC2 5.75 or 11 remainder 1 |
Additional guidance
| \(46 \div 2 = 25\), (\(25 \div 2 =\)) 12.5 | M1M1A0 |
| \(46 \div 2 = 24\), followed by 11 | M1M0A0 |
| 11.5 in working, different answer on answer line (do not ignore further work) | M1M1A0 |
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1 | ||
| \(34 - k\) or \(34 - 10\) or 24 | M1 | oe implied by \(34 - 2k\) or \(34 - 3k\) |
| \(3k = 34 - 10\) or \(3k =\) their 24 or \(\dfrac{34 - 10}{3}\) or \(\dfrac{\text{their } 24}{3}\) | M1dep | oe |
| 8 | A1 | SC2 \(-8\) or all terms seen 34, 26, 18, 10 SC1 6 |
| Alternative method 2 | ||
| \(10 + k\) or \(34 - 10\) or 24 | M1 | oe implied by \(10 + 2k\) or \(10 + 3k\) |
| \(10 + 3k = 34\) or \(3k =\) their 24 or \(\dfrac{34 - 10}{3}\) or \(\dfrac{\text{their } 24}{3}\) | M1dep | oe |
| 8 | A1 | SC2 \(-8\) or all terms seen 34, 26, 18, 10 SC1 6 |
| Alternative method 3 | ||
| One correct trial | M1 | a correct trial is either a subtraction of the same value, exactly three times, from 34 and evaluated correctly or addition of the same value, exactly three times, from 10 and evaluated correctly |
| Two or more correct trials | M1dep | |
| 8 | A1 | SC2 \(-8\) or all terms seen 34, 26, 18, 10 SC1 6 |
Additional guidance
Accept any letter in place of \(k\)