// Numbas version: finer_feedback_settings
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u_1}</p>\n<p style=\"text-align: left;\">(b) Using the nth term formula u_n = u_1 + (n - 1)d with n = {n}, we get</p>\n<p style=\"text-align: center;\">u_8 = u_1 + ({n} - 1)d</p>\n<p style=\"text-align: center;\">u_8 = {u_1} + (8 - 1)({d})</p>\n<p style=\"text-align: center;\">u_8 = {u_1 + (8 - 1)(d)}</p>\n<p style=\"text-align: left;\">c) Using the sum of n terms formula S_n = (n/2)(u_1 + u_n) with n = {n}, we obtain</p>\n<p style=\"text-align: center;\">S_8 = ({n}/2)({u_1} + {u_8})</p>\n<p style=\"text-align: center;\">S_8 = {(n/2)(u_1 + (u_8))}</p>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"u_1": {"name": "u_1", "group": "Ungrouped variables", "definition": "random(0 .. 100#1)", "description": "", "templateType": "randrange", "can_override": false}, "u_2": {"name": "u_2", "group": "Ungrouped variables", "definition": "random(0 .. 100#1)", "description": "", "templateType": "randrange", "can_override": false}, "u_3": {"name": "u_3", "group": "Ungrouped variables", "definition": "random(0 .. 100#1)", "description": "", "templateType": "randrange", "can_override": false}, "n": {"name": "n", "group": "Ungrouped variables", "definition": "8", "description": "", "templateType": "number", "can_override": false}, "d": {"name": "d", "group": "Ungrouped variables", "definition": "u_2 - 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1)*d", "maxValue": "u_1 + (n - 1)*d", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "S_8 is", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "(n/2)*(u_1 + u_8)", "maxValue": "(n/2)*(u_1 + u_8)", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "contributors": [{"name": "Nguyen Hai Anh", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/30342/"}], "resources": []}]}], "contributors": [{"name": "Nguyen Hai Anh", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/30342/"}]}