/maths/ccea/grade-4-4-7-sequences-nth-term/questions","formulaUrl":null,"initialIndex":23,"initialQuestionWindow":[{"id":"ffc74084-c4a8-4159-a5c8-a84a39039348","revisionId":"018f5434-b838-41fe-b980-180489cd1948","questionNumber":null,"questionType":"LA","specification":"Here are the first five terms of a sequence.\n\n$1, 2, 4, 7, 11$","difficulty":1,"difficultyBand":"medium","totalMarks":2,"sourceTitle":null,"calculatorUse":"non_calc","parts":[{"id":"196bd944-79e8-415a-a35f-5f4e8762b597","label":"a","content":"Write down the next two terms in the sequence.","markscheme":"- Identifies the pattern of increasing differences ($+1, +2, +3, +4$) M1\n- Correctly calculates the next two terms: $11 + 5 = 16$ and $16 + 6 = 22$ A1","marks":2,"order":0,"markingRubric":{"totalMarks":2,"points":[{"id":"p1","marks":1,"description":"Identifies the pattern of increasing differences ($+1, +2, +3, +4$).","code":"M"},{"id":"p2","marks":1,"description":"Correctly calculates the next two terms: 16 and 22.","code":"A"}],"finalAnswers":["16 and 22","16, 22"],"generatedAt":"2026-05-06T14:05:26.545Z","modelVersion":"gemini-3-flash-preview"},"explanation":{"methods":[{"id":"increasing_differences","label":"Increasing differences","steps":[{"type":"text","order":0,"title":"Find the differences","content":"Look at how much is added each time:\n\n$$1\\xrightarrow{+1}2\\xrightarrow{+2}4\\xrightarrow{+3}7\\xrightarrow{+4}11$$\n\nThe differences increase by $1$ each time. Identifying this pattern earns **M1**.","highlights":[{"text":"$$1, 2, 4, 7, 11$","location":"specification"}]},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$11+\\color{@sky}{5}=\\color{@green}{16}$"},{"latex":"\\color{@green}{16}+\\color{@orange}{6}=\\color{@purple}{22}$"}]},"order":1,"title":"Continue the pattern","description":"The next amounts to add are five and then six. This gives the next two terms, 16 and 22, so obtaining both correct terms earns the A1 mark."}]}],"generatedAt":"2026-07-19T16:08:23.741Z","modelVersion":"gpt-5.6-sol","explanationVersion":"v3"},"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":null},{"id":"16b66ab1-60d9-4fce-a348-4d0b1691f993","revisionId":"60517922-667f-4f62-bbae-f417edec08e6","questionNumber":null,"questionType":"LA","specification":"Here are the first 5 terms of a sequence.\n\n10, 17, 24, 31, 38","difficulty":1,"difficultyBand":"medium","totalMarks":3,"sourceTitle":null,"calculatorUse":"non_calc","parts":[{"id":"f581791e-d359-416c-a683-05b07ae5dd4e","label":"a","content":"Find the next term of this sequence.","markscheme":"- Adds 7 to the last term: $38 + 7 = 45$ B1","marks":1,"order":0,"markingRubric":{"totalMarks":1,"points":[{"id":"p1","marks":1,"description":"Adds 7 to the last term to find 45.","code":"B"}],"finalAnswers":["45"],"generatedAt":"2026-05-06T14:06:26.543Z","modelVersion":"gemini-3-flash-preview"},"explanation":{"methods":[{"id":"add_common_difference","label":"Add the common difference","steps":[{"type":"text","order":0,"title":"Find the difference","content":"Compare neighbouring terms: each term is $7$ more than the one before, so the sequence rule is **add $7$**.","highlights":[{"text":"10, 17, 24, 31, 38","location":"specification"}]},{"type":"text","order":1,"title":"Add seven","content":"Apply the same rule to the final given term:\n\n$$38+7=45$$\n\nSo the next term is $45$. This earns the B1 mark."}]}],"generatedAt":"2026-07-19T19:21:16.285Z","modelVersion":"gpt-5.6-sol","explanationVersion":"v3"},"options":[]},{"id":"5e4d0ce8-1d05-4a22-b487-8bda02d3ca73","label":"b","content":"The $n$th term of a different sequence is $3n^2 - 2$. Work out the 5th term of this sequence.","markscheme":"- Substitutes $n=5$: $3(5^2) - 2$ M1\n- $3(25) - 2 = 73$ A1","marks":2,"order":1,"markingRubric":{"totalMarks":2,"points":[{"id":"p1","marks":1,"description":"Evidence of substitution of n = 5 into the expression.","code":"M"},{"id":"p2","marks":1,"description":"Correct evaluation to 73.","code":"A"}],"finalAnswers":["73"],"generatedAt":

Sequences (Nth Term)

Question 16

Sequences (Nth Term) Questions

Sequences (Nth Term)

Question 16

Sequences (Nth Term) Questions