{"paper":{"id":"site-2652","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"podstawowa","variant":null,"exam_pdf":null,"key_pdf":null,"question_count":10,"source_label":"Matematyka · Zbiory zadań (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},"questions":[{"id":"site-2652/zad/3132","paper_id":"site-2652","number":"3132","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"podstawowa","text":"Trzeci wyraz ciągu geometrycznego jest równy 4, a czwarty wyraz tego ciągu jest równy (-2). Pierwszy wyraz tego ciągu jest równy A. 16 B. -16 C. 8 D. -8","answer":null,"answer_text":null,"solution":null,"image":"img/site/2652/zad-3132.svg","solution_image":"img/site/2652/rozw-3132.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-2652/zad/3133","paper_id":"site-2652","number":"3133","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"podstawowa","text":"Trzeci wyraz ciągu geometrycznego jest równy 4, a piąty wyraz tego ciągu jest równy 1. Pierwszy wyraz tego ciągu jest równy A. 4, B. 4 pierwiastki z 2 C. 16 D. 16 pierwiastków z 2","answer":null,"answer_text":null,"solution":null,"image":"img/site/2652/zad-3133.svg","solution_image":"img/site/2652/rozw-3133.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-2652/zad/3134","paper_id":"site-2652","number":"3134","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"podstawowa","text":"Liczby -8, 4, x+1 (w podanej kolejności) są pierwszym, drugim i trzecim wyrazem ciągu geometrycznego. Wówczas liczba x jest równa A. -3, B. -1.5, C. 1, D. 15","answer":null,"answer_text":null,"solution":null,"image":"img/site/2652/zad-3134.svg","solution_image":"img/site/2652/rozw-3134.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-2652/zad/3294","paper_id":"site-2652","number":"3294","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"podstawowa","text":"W ciągu geometrycznym (a_n) dane są a_2 = pierwiastek z 3 / 2 i a_3 = - 3/2. Wtedy wyraz a_1 jest równy A. -1/2, B. 1/2, C. -pierwiastek z 3 / 2, D. pierwiastek z 3 / 3","answer":null,"answer_text":null,"solution":null,"image":"img/site/2652/zad-3294.svg","solution_image":"img/site/2652/rozw-3294.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-2652/zad/4355","paper_id":"site-2652","number":"4355","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"podstawowa","text":"Dany jest ciąg geometryczny (a_n), w którym a_1 = -pierwiastek z 2, a_2 = 2, a_3 = -2 * pierwiastek z 2. Dziesiąty wyraz tego ciągu, czyli a_{10}, jest równy A. 32, B. -32, C. 16 * pierwiastek z 2, D. -16 * pierwiastek z 2.","answer":null,"answer_text":null,"solution":null,"image":"img/site/2652/zad-4355.svg","solution_image":"img/site/2652/rozw-4355.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-2652/zad/5474","paper_id":"site-2652","number":"5474","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"podstawowa","text":"Rozwiązanie zadania. Ciąg (x,y,z) jest geometryczny. Iloczyn wszystkich wyrazów tego ciągu jest równy 64. Stąd wynika, że y jest równe A. 3/64 B. 64/3 C. 4 D. 3","answer":null,"answer_text":null,"solution":null,"image":"img/site/2652/zad-5474.svg","solution_image":"img/site/2652/rozw-5474.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-2652/zad/6888","paper_id":"site-2652","number":"6888","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"podstawowa","text":"Dane są liczby: a=2√2, b=4, c=4√2. Dokończ zdanie tak, aby było prawdziwe. Wybierz odpowiedź A albo B oraz jej uzasadnienie 1., 2. albo 3. Liczby a, b oraz c tworzą w podanej kolejności A. ciąg arytmetyczny, B. ciąg geometryczny, ponieważ 1. b=a+c/2 2. b=(c-a)^2/2 3. b²=a⋅c","answer":null,"answer_text":null,"solution":null,"image":"img/site/2652/zad-6888.svg","solution_image":"img/site/2652/rozw-6888.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-2652/zad/7255","paper_id":"site-2652","number":"7255","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"podstawowa","text":"W dziewięciowyrazowym ciągu geometrycznym o wyrazach dodatnich pierwszy wyraz jest równy 3, a ostatni wyraz jest równy 12. Piąty wyraz tego ciągu jest równy A. 3 4√2 B. 6 C. 7 1/2 D. 8 1/2","answer":null,"answer_text":null,"solution":null,"image":"img/site/2652/zad-7255.svg","solution_image":"img/site/2652/rozw-7255.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-2652/zad/8152","paper_id":"site-2652","number":"8152","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/2652/zad-8152.svg","solution_image":"img/site/2652/rozw-8152.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-2652/zad/8154","paper_id":"site-2652","number":"8154","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"podstawowa","text":"Trzywyrazowy ciąg (x, x+4, 2x+8), o wszystkich wyrazach dodatnich, jest geometryczny. Iloraz tego ciągu jest równy A. (-4) B. (-1) C. 2 D. 4","answer":null,"answer_text":null,"solution":null,"image":"img/site/2652/zad-8154.svg","solution_image":"img/site/2652/rozw-8154.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"}]}