d Series (A-level only) Flashcards","topicId":"d498fb7e-4189-4089-8881-535baad3ce4f","topicSlug":"sequences-and-series-6","cards":[{"id":"061a41c0-3987-42f5-a3c4-242181105050","cardType":"basic","front":"What does $u_{10}$ represent?","back":"The tenth term of the sequence.","points":1,"mcqOptions":null},{"id":"63491b9b-6a3f-424b-b476-609ef0e8df5c","cardType":"basic","front":"How is the series associated with a sequence formed?","back":"By adding the sequence's terms.","points":1,"mcqOptions":null},{"id":"74a058d7-6928-4f84-a013-638b6bffb334","cardType":"basic","front":"What is the common ratio of $5,15,45,135,\\ldots$?","back":"$r=3$.","points":1,"mcqOptions":null},{"id":"4d120c32-21b7-4607-98e3-808e7f739132","cardType":"basic","front":"Why does a constant difference not prove that a sequence is geometric?","back":"A geometric sequence requires a constant ratio.","points":2,"mcqOptions":null},{"id":"cd3ff8c4-b704-48a4-9dcc-8e177be9c79b","cardType":"basic","front":"What happens to successive non-zero terms when a geometric sequence has $r<0$?","back":"Their signs alternate.","points":1,"mcqOptions":null},{"id":"e771ef75-b014-482b-8d70-5ac598da2859","cardType":"cloze","front":"For positive terms, $0<r<1$ produces terms that [ ], while $r>1$ produces terms that increase.","back":"For positive terms, $0<r<1$ produces terms that decrease towards zero, while $r>1$ produces terms that increase.","points":null,"mcqOptions":null},{"id":"e410715d-a9db-4b44-85ca-0134ff265c9f","cardType":"cloze","front":"For positive terms, $0<r<1$ produces terms that decrease towards zero, while $r>1$ produces terms that [ ].","back":"For positive terms, $0<r<1$ produces terms that decrease towards zero, while $r>1$ produces terms that increase.","points":null,"mcqOptions":null},{"id":"a01a6b3d-b4be-42b2-9cfa-7345fafad972","cardType":"cloze","front":"A geometric sequence with first term $a$ and common ratio $r$ has nth term $\\text{[...]}$.","back":"A geometric sequence with first term $a$ and common ratio $r$ has nth term $\\boxed{u_n=ar^{n-1}}$.","points":null,"mcqOptions":null},{"id":"760e8283-ca6a-4863-bf7f-88125fad0e66","cardType":"basic","front":"Why is the exponent in $u_n=ar^{n-1}$ equal to $n-1$?","back":"Term $n$ contains $n-1$ factors of $r$.","points":2,"mcqOptions":null},{"id":"82c68169-67e4-45a7-9a48-53e1869ce10a","cardType":"basic","front":"Find $u_8$ for $160,80,40,\\ldots$.","back":"$u_8=160\\left(\\frac12\\right)^7=\\frac54$.","points":2,"mcqOptions":null},{"id":"2457ac29-716a-4f21-bcb7-e95c3d677efb","cardType":"basic","front":"Which term of $3,6,12,\\ldots$ is $384$?","back":"The eighth term, since $3\\cdot2^7=384$.","points":2,"mcqOptions":null},{"id":"fdd657f9-1a1a-47dc-bf78-23e93439c210","cardType":"cloze","front":"A repeated increase of $p$% uses $\\text{[...]}$, while a repeated decrease uses $r=1-\\frac{p}{100}$.","back":"A repeated increase of $p$% uses $\\boxed{r=1+\\frac{p}{100}}$, while a repeated decrease uses $r=1-\\frac{p}{100}$.","points":null,"mcqOptions":null},{"id":"86b3c689-3191-49a5-9c28-e424943bc4ca","cardType":"cloze","front":"A repeated increase of $p$% uses $r=1+\\frac{p}{100}$, while a repeated decrease uses $\\text{[...]}$.","back":"A repeated increase of $p$% uses $r=1+\\frac{p}{100}$, while a repeated decrease uses $\\boxed{r=1-\\frac{p}{100}}$.","points":null,"mcqOptions":null},{"id":"37604a1c-77ef-419c-968c-0a4ea

3.4.5 Sequences and Series (A-level only) Flashcards

3.4.5 Sequences and Series (A-level only) Flashcards