// Numbas version: exam_results_page_options {"name": "Simon's copy of Write down and apply the formula for an arithmetic sequence.", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "

Given the first few terms of an arithmetic sequence, write down its formula, then find a couple of particular terms.

"}, "tags": [], "ungrouped_variables": ["a1", "d", "small", "large"], "variable_groups": [], "variables": {"d": {"definition": "random(3..13 except 10)", "name": "d", "group": "Ungrouped variables", "description": "", "templateType": "anything"}, "a1": {"definition": "random(1..90)", "name": "a1", "group": "Ungrouped variables", "description": "

The first term in the sequence

", "templateType": "anything"}, "small": {"definition": "random(6..10)", "name": "small", "group": "Ungrouped variables", "description": "

A small index to compute

", "templateType": "anything"}, "large": {"definition": "random(10..50#5)*10", "name": "large", "group": "Ungrouped variables", "description": "

A large index to compute

", "templateType": "anything"}}, "name": "Simon's copy of Write down and apply the formula for an arithmetic sequence.", "parts": [{"showCorrectAnswer": true, "gaps": [{"showCorrectAnswer": true, "showFeedbackIcon": true, "answer": "{a1}+(n-1){d}", "unitTests": [], "scripts": {}, "answerSimplification": "basic", "vsetRange": [0, 1], "expectedVariableNames": [], "type": "jme", "customMarkingAlgorithm": "", "checkingType": "absdiff", "showPreview": true, "failureRate": 1, "marks": 1, "checkingAccuracy": 0.001, "vsetRangePoints": 5, "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "checkVariableNames": false, "variableReplacementStrategy": "originalfirst"}], "showFeedbackIcon": true, "unitTests": [], "scripts": {}, "type": "gapfill", "customMarkingAlgorithm": "", "prompt": "

Write out an expression for $a_n$, the $n^{\\text{th}}$ term of the sequence, in terms of $n$.

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$a_n =$ [[0]]

\n

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Find the $\\var{small}^{\\text{th}}$ term

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$a_{\\var{small}} =$ [[0]]

\n

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Find the $\\var{large}^{\\text{th}}$ term

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$a_{\\var{large}} =$[[0]]

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In this question, consider the sequence

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\$a = \\var{a1}, \\; \\var{a1+d}, \\; \\var{a1+d*2}, \\; \\var{a1+d*3}, \\; \\ldots \$

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A helpful person has drawn out a table of the terms so far.

\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
 $\\boldsymbol{n}$ $\\boldsymbol{a_n}$ $1$ $2$ $3$ $4$ $\\ldots$ $\\var{a1}$ $\\var{a1+d}$ $\\var{a1+2d}$ $\\var{a1+3d}$ $\\ldots$
", "functions": {}, "variablesTest": {"condition": "", "maxRuns": 100}, "extensions": [], "advice": "

The formula for the $n^\\text{th}$ term, $a_n$, of an arithmetic sequence is

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\$a_n=a_1+(n-1)d \\text{.} \$

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$a_1$ is the first term, and $d$ is the common difference between adjacent terms.

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a)

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In the given sequence, the common difference is $\\var{a1+d} - \\var{a1} = \\var{d}$, and the first term is $\\var{a1}$.

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So, the formula for this sequence is

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\$a_n = \\var{a1} + (n-1) \\times \\var{d} \\text{.} \$

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(which can be simplified to $a_n = \\simplify{{a1} + {d}n-{d}}$ if desired)

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b)

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\$a_\\var{small} = \\var{a1} + (\\var{small}-1) \\times \\var{d} = \\var{a1+(small-1)*d} \\text{.} \$

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c)

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\$a_\\var{large} = \\var{a1} + (\\var{large}-1) \\times \\var{d} = \\var{a1+(large-1)*d} \\text{.} \$

\n\n", "type": "question", "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Simon Thomas", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3148/"}]}]}], "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Simon Thomas", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3148/"}]}