evel only) Flashcards","topicId":"d264cadd-8ba8-4fed-81a5-d822e191c5d5","topicSlug":"types-of-sequence","cards":[{"id":"f2cd980c-057c-43cb-9786-5c7fbb51bc5c","cardType":"basic","front":"How is $x_k$ found from an nth-term formula?","back":"Substitute $n=k$ into the formula.","points":1,"mcqOptions":null},{"id":"56797722-2975-4b9c-81e4-8a9485fb81d7","cardType":"basic","front":"Why must an initial value accompany a recurrence relation?","back":"It provides the first term from which later terms are generated.","points":2,"mcqOptions":null},{"id":"626ca8da-bcbe-4de9-b19c-834ef573eabb","cardType":"basic","front":"In $x_{n+1}=3x_n-2$, what input is used to generate the next term?","back":"The current term value $x_n$.","points":1,"mcqOptions":null},{"id":"2305f1f3-630b-4ada-9b56-f2d0fca7b8b9","cardType":"basic","front":"For $x_n=3n^2-2$, calculate $x_{10}$.","back":"$x_{10}=298$.","points":1,"mcqOptions":null},{"id":"f6da60e3-b5ca-42f4-b5bb-cb5019dbe1ff","cardType":"basic","front":"Given $x_1=4$ and $x_{n+1}=3x_n-2$, calculate $x_4$.","back":"$x_4=82$.","points":1,"mcqOptions":null},{"id":"2a92cd32-5c92-4b39-8ff8-e4aaa4d00420","cardType":"cloze","front":"A sequence is strictly increasing when $\\text{[...]}$ for every permitted $n$.","back":"A sequence is strictly increasing when $\\boxed{x_{n+1}>x_n}$ for every permitted $n$.","points":null,"mcqOptions":null},{"id":"ff50b05f-f592-4bb1-9122-653f023beb36","cardType":"basic","front":"What feature distinguishes a non-decreasing sequence from a strictly increasing sequence?","back":"A non-decreasing sequence allows consecutive terms to be equal.","points":1,"mcqOptions":null},{"id":"272afe93-b389-45fb-97b9-4c0532e91e4f","cardType":"cloze","front":"A sequence is strictly decreasing when $\\text{[...]}$ for every permitted $n$.","back":"A sequence is strictly decreasing when $\\boxed{x_{n+1}allows consecutive terms to be equal.","points":1,"mcqOptions":null},{"id":"a9c1dd65-aaac-44cb-9fdc-f37afedf6302","cardType":"cloze","front":"If $x_{n+1}-x_n$ is [ ] for every permitted $n$, the sequence is strictly increasing. If it is negative, the sequence is strictly decreasing.","back":"If $x_{n+1}-x_n$ is positive for every permitted $n$, the sequence is strictly increasing. If it is negative, the sequence is strictly decreasing.","points":null,"mcqOptions":null},{"id":"c4b2ac4f-4097-4eef-9089-8c5aff07640f","cardType":"cloze","front":"If $x_{n+1}-x_n$ is positive for every permitted $n$, the sequence is strictly increasing. If it is [ ], the sequence is strictly decreasing.","back":"If $x_{n+1}-x_n$ is positive for every permitted $n$, the sequence is strictly increasing. If it is negative, the sequence is strictly decreasing.","points":null,"mcqOptions":null},{"id":"1b9b5746-25ad-4ae1-b8d4-d824874dd137","cardType":"basic","front":"Classify $x_n=n^2-4n$ for $n\\geq1$ using $x_{n+1}-x_n=2n-3$.","back":"Neither - it first decreases, then increases.","points":2,"mcqOptions":null},{"id":"fb369c6c-cd13-48c4-bf58-ed9c87a585ad","cardType":"basic","front":"Why does a sequence containing negative terms not have to be decreasing?","back":"Direction depends on consecutive-term comparisons, not the terms' signs.","points":2,"mcqOptions":null},{"id":"cdae30bf-919d-4941-9d38-8976e72f1942","cardType":"cloze","front":"A sequence has period $p$ if $\\text{[...]}$ for every permitted $n$.","back":"A sequence has period $p$ if $\\boxed{x_{n+p}=x_n}$ for every permitted $n$.","points":

1.7.2 Types of sequence (A-level only) Flashcards

1.7.2 Types of sequence (A-level only) Flashcards