// Numbas version: exam_results_page_options
{"name": "Arithmetic Sequence - Work with any two terms", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Arithmetic Sequence - Work with any two terms", "tags": [], "metadata": {"description": "Given two (not necessarily consecutive) terms in an arithmetic sequence, evaluate the common difference, first term and then apply to find sum of a number of terms.&nbsp; (Working with integer terms only)", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p>In an arithmetic sequence the {term_a} term is {u_a} and the {term_b} is {u_b}.</p>", "advice": "<p>In part (a) you should divide the difference between the {term_b} term and the {term_a} term by {n}</p>\n<p>({u_b}-{u_a})/{n} = {d}</p>\n<p>In part (b) use the formula</p>\n<p>$u_n = u_1&nbsp; + (n-1)d$&nbsp;</p>\n<p>and rearrange to find $u_1$ either using the {term_a} or {term_b} term and calculated value of $d$</p>\n<p>$u_1 =$ {u_1}</p>\n<p>In part c use the formula for the sum of n terms of an arithmetic sequence</p>\n<p>$S_n = \\frac{n}{2}(2u_1+(n-1)d)$</p>\n<p>In this case the sum of the first {number_sum} terms is</p>\n<p>= ({terms_to_sum}/2) x (2 x {u_1} + ({terms_to_sum} - 1) x {d}))</p>\n<p>= {sum_val}</p>\n<p></p>", "rulesets": {}, "extensions": [], "variables": {"term_a": {"name": "term_a", "group": "Ungrouped variables", "definition": "\"{terms_eng[{a}-1]}\"", "description": "<p>english word for the term number given first in problem.</p>", "templateType": "string"}, "a": {"name": "a", "group": "Ungrouped variables", "definition": "random(3 .. 7#1)", "description": "<p>number of smaller term given in problem.</p>", "templateType": "randrange"}, "terms_eng": {"name": "terms_eng", "group": "Ungrouped variables", "definition": "[ \"first\", \"second\", \"third\", \"fourth\", \"fifth\", \"sixth\", \"seventh\", \"eighth\", \"ninth\", \"tenth\", \"eleventh\", \"twelfth\", \"thirteenth\" ]", "description": "<p>list to convert numbers to word for term</p>", "templateType": "list of strings"}, "d": {"name": "d", "group": "Ungrouped variables", "definition": "random(2 .. 6#1)", "description": "<p>Common difference in this sequence.</p>", "templateType": "randrange"}, "n": {"name": "n", "group": "Ungrouped variables", "definition": "random(2 .. 5#1)", "description": "<p>difference in terms of number of terms</p>", "templateType": "randrange"}, "u_a": {"name": "u_a", "group": "Ungrouped variables", "definition": "{u_1}+({a}-1)*{d}", "description": "<p>value of ath term</p>", "templateType": "anything"}, "u_1": {"name": "u_1", "group": "Ungrouped variables", "definition": "random(2 .. 7#0.5)", "description": "<p>First term in this sequence</p>", "templateType": "randrange"}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "{a}+{n}", "description": "<p>term number of larger term in sequence</p>", "templateType": "anything"}, "u_b": {"name": "u_b", "group": "Ungrouped variables", "definition": "{u_1}+({b}-1)*{d}", "description": "<p>value of bth term</p>", "templateType": "anything"}, "term_b": {"name": "term_b", "group": "Ungrouped variables", "definition": "\"{terms_eng[{b}-1]}\"", "description": "<p>term number in words</p>", "templateType": "string"}, "number_eng": {"name": "number_eng", "group": "Ungrouped variables", "definition": "[ \"one\", \"two\", \"three\", \"four\", \"five\", \"six\", \"seven\", \"eight\", \"nine\", \"ten\", \"eleven\", \"twelve\", \"thirteen\", \"fourteen\", \"fifteen\", \"sixteen\", \"seventeen\", \"eighteen\", \"nineteen\", \"twenty\", \"twentyone\", \"twentytwo\", \"twentythree\", \"twentyfour\", \"twentyfive\" ]", "description": "<p>table to convert numbers to words</p>", "templateType": "list of strings"}, "terms_to_sum": {"name": "terms_to_sum", "group": "Ungrouped variables", "definition": "random(15 .. 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