{"id":503,"date":"2020-01-12T20:42:48","date_gmt":"2020-01-12T20:42:48","guid":{"rendered":"http:\/\/localhost\/?post_type=knowledgebase&p=503"},"modified":"2024-02-07T13:56:26","modified_gmt":"2024-02-07T13:56:26","slug":"practice-question-sequence-and-series","status":"publish","type":"knowledgebase","link":"https:\/\/ibalmaths.com\/index.php\/ibdp-math-hl-2\/sequence-and-series\/practice-question-sequence-and-series\/","title":{"rendered":"Sequence and Series – Practice Questions"},"content":{"rendered":"

Q1. Suppose \r\nα<\/mi>,<\/mo> <\/mo>β<\/mi><\/math>\r\n are the roots of \r\nx<\/mi>2<\/mn><\/msup>+<\/mo>k<\/mi>x<\/mi>+<\/mo>1<\/mn>=<\/mo>0<\/mn><\/math>\r\n and \r\nγ<\/mi>,<\/mo> <\/mo>δ<\/mi><\/math>\r\n are the roots of \r\nx<\/mi>2<\/mn><\/msup>+<\/mo>x<\/mi>+<\/mo>k<\/mi>=<\/mo>0<\/mn><\/math>\r\n .<\/p>\r\n

(a)<\/strong> if \r\nα<\/mi>,<\/mo> <\/mo>β<\/mi>,<\/mo> <\/mo>γ<\/mi>,<\/mo> <\/mo>δ<\/mi><\/math>\r\n are in arithmetic sequence, then find the common difference of this arithmetic sequence in terms of \r\nk<\/mi><\/math>\r\n ,<\/p>\r\n

(b)<\/strong> if \r\nα<\/mi>,<\/mo> <\/mo>β<\/mi>,<\/mo> <\/mo>γ<\/mi>,<\/mo> <\/mo>δ<\/mi><\/math>\r\n are in geometric sequence, then find the common ratio of this geometric sequence in terms of \r\nk<\/mi><\/math>\r\n .<\/p>\r\n