{"paper":{"id":"site-2679","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"podstawowa","variant":null,"exam_pdf":null,"key_pdf":null,"question_count":8,"source_label":"Matematyka · Zbiory zadań (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},"questions":[{"id":"site-2679/zad/3128","paper_id":"site-2679","number":"3128","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"podstawowa","text":"Ciąg (a_n) jest określony wzorem a_n=(-1)^n(n^2-2n) dla n>=1. Wtedy A. a_3>0 B. a_3=3 C. a_3<2 a_3=2","answer":null,"answer_text":null,"solution":null,"image":"img/site/2679/zad-3128.svg","solution_image":"img/site/2679/rozw-3128.svg","topics":null,"page_from":null,"source":"site","answer_source":null,"answer_text_source":null,"solution_source":null,"text_source":"site","source_label":"Matematyka · Zbiory zadań (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-2679/zad/3129","paper_id":"site-2679","number":"3129","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"podstawowa","text":"Ciąg (a_n) jest określony wzorem a_n=(-3)^n*(9-n^2) dla n>=1. Wynika stąd, że A. a_3=-81 B. a_3=-27 C. a_3=0 D. a_3>0","answer":null,"answer_text":null,"solution":null,"image":"img/site/2679/zad-3129.svg","solution_image":"img/site/2679/rozw-3129.svg","topics":null,"page_from":null,"source":"site","answer_source":null,"answer_text_source":null,"solution_source":null,"text_source":"site","source_label":"Matematyka · Zbiory zadań (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-2679/zad/4356","paper_id":"site-2679","number":"4356","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"podstawowa","text":"Ciąg (a_n) jest określony wzorem a_n = 24-4n / n dla n >= 1. Liczba wszystkich całkowitych nieujemnych wyrazów tego ciągu jest równa A. 7, B. 6, C. 5, D. 4.","answer":null,"answer_text":null,"solution":null,"image":"img/site/2679/zad-4356.svg","solution_image":"img/site/2679/rozw-4356.svg","topics":null,"page_from":null,"source":"site","answer_source":null,"answer_text_source":null,"solution_source":null,"text_source":"site","source_label":"Matematyka · Zbiory zadań (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-2679/zad/5314","paper_id":"site-2679","number":"5314","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"podstawowa","text":"Ciąg (a_n) jest określony wzorem a_n = 2n^2 dla n≥1. Różnica a_5 - a_4 jest równa A. 4; B. 20; C. 36; D. 18.","answer":null,"answer_text":null,"solution":null,"image":"img/site/2679/zad-5314.svg","solution_image":"img/site/2679/rozw-5314.svg","topics":null,"page_from":null,"source":"site","answer_source":null,"answer_text_source":null,"solution_source":null,"text_source":"site","source_label":"Matematyka · Zbiory zadań (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-2679/zad/5478","paper_id":"site-2679","number":"5478","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"podstawowa","text":"Rozwiązanie zadania. Ciąg (a_n) jest określony wzorem a_n = (-2)^n⋅ n + 1 dla każdej liczby naturalnej n≥1. Wtedy trzeci wyraz tego ciągu jest równy A. -24 B. -17 C. -32 D. -23","answer":null,"answer_text":null,"solution":null,"image":"img/site/2679/zad-5478.svg","solution_image":"img/site/2679/rozw-5478.svg","topics":null,"page_from":null,"source":"site","answer_source":null,"answer_text_source":null,"solution_source":null,"text_source":"site","source_label":"Matematyka · Zbiory zadań (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-2679/zad/6724","paper_id":"site-2679","number":"6724","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"podstawowa","text":"Dokończ zdanie. Wybierz odpowiedź A, B albo C oraz jej uzasadnienie 1., 2. albo 3. Ciąg (a_n) określony wzorem a_n=n^2-n dla każdej liczby naturalnej n≥1 jest A. rosnący, B. malejący, C. stały, ponieważ dla każdej liczby naturalnej n≥1 1. różnica a_{n+1}-a_n jest liczbą ujemną. 2. różnica a_{n+1}-a_n jest równa zero. 3. różnica a_{n+1}-a_n jest liczbą dodatnią.","answer":null,"answer_text":null,"solution":null,"image":"img/site/2679/zad-6724.svg","solution_image":"img/site/2679/rozw-6724.svg","topics":null,"page_from":null,"source":"site","answer_source":null,"answer_text_source":null,"solution_source":null,"text_source":"site","source_label":"Matematyka · Zbiory zadań (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-2679/zad/7256","paper_id":"site-2679","number":"7256","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"podstawowa","text":"Ciąg (a_n) jest określony wzorem a_n=(n+3)(n-5). Liczba ujemnych wyrazów tego ciągu jest równa A. 3 B. 4 C. 7 D. 9","answer":null,"answer_text":null,"solution":null,"image":"img/site/2679/zad-7256.svg","solution_image":"img/site/2679/rozw-7256.svg","topics":null,"page_from":null,"source":"site","answer_source":null,"answer_text_source":null,"solution_source":null,"text_source":"site","source_label":"Matematyka · Zbiory zadań (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-2679/zad/8151","paper_id":"site-2679","number":"8151","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"podstawowa","text":"Ciąg (a_n) jest określony wzorem a_n = 32⋅(1/2)^n-5 dla każdej liczby naturalnej n≥1. Trzeci wyraz ciągu (a_n) jest równy A. 8 B. 64 C. 128 D. 256","answer":null,"answer_text":null,"solution":null,"image":"img/site/2679/zad-8151.svg","solution_image":"img/site/2679/rozw-8151.svg","topics":null,"page_from":null,"source":"site","answer_source":null,"answer_text_source":null,"solution_source":null,"text_source":"site","source_label":"Matematyka · Zbiory zadań (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"}]}