{"paper":{"id":"site-4930","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"rozszerzona","variant":null,"exam_pdf":null,"key_pdf":null,"question_count":2,"source_label":"Matematyka · Zbiory zadań (rozszerzona)","subject_label":"Matematyka","category_label":"Zbiory zadań"},"questions":[{"id":"site-4930/zad/5346","paper_id":"site-4930","number":"5346","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"rozszerzona","text":"W trzywyrazowym ciągu geometrycznym (a_1,a_2,a_3) spełniona jest równość a_1 + a_2 + a_3 = 21/4. Wyrazy a_1, a_2, a_3 są - odpowiednio - czwartym, drugim i pierwszym wyrazem rosnącego ciągu arytmetycznego. Oblicz a_1.","answer":null,"answer_text":null,"solution":null,"image":"img/site/4930/zad-5346.svg","solution_image":"img/site/4930/rozw-5346.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 (rozszerzona)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-4930/zad/5511","paper_id":"site-4930","number":"5511","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"rozszerzona","text":"Rozwiązywanie zadania. Czterowyrazowy ciąg (a,b,c,d) jest rosnący i arytmetyczny. Kwadrat największego wyrazu tego ciągu jest równy podwojonej sumie kwadratów pozostałych wyrazów tego ciągu. Ponadto ciąg (a+100,b,c) jest geometryczny. Oblicz wyrazy ciągu a,b,c,d.","answer":null,"answer_text":null,"solution":null,"image":"img/site/4930/zad-5511.svg","solution_image":"img/site/4930/rozw-5511.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 (rozszerzona)","subject_label":"Matematyka","category_label":"Zbiory zadań"}]}