{"id":1724,"date":"2020-04-15T10:34:11","date_gmt":"2020-04-15T10:34:11","guid":{"rendered":"http:\/\/ibalmaths.com\/?post_type=knowledgebase&#038;p=1724"},"modified":"2020-04-15T10:34:37","modified_gmt":"2020-04-15T10:34:37","slug":"activity-sequences-ad-series","status":"publish","type":"knowledgebase","link":"https:\/\/ibalmaths.com\/index.php\/ibdp-math-hl-2\/sequence-and-series\/activity-sequences-ad-series\/","title":{"rendered":"Activity &#8211; Sequences and Series"},"content":{"rendered":"<p>1. To understand the concept of arithmetic sequence sketch the graph of some linear functions using some graphing software ( I used DESMOS). You will observe that when \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>n<\/mi><mo>=<\/mo><mn>1<\/mn><mo>,<\/mo><mo>&#160;<\/mo><mn>2<\/mn><mo>,<\/mo><mo>&#160;<\/mo><mn>3<\/mn><mo>,<\/mo><mo>&#160;<\/mo><mo>.<\/mo><mo>.<\/mo><mo>.<\/mo><mo>.<\/mo><mo>.<\/mo><\/math>\r\n the y-values will change increase\/decrease with a constant number. Try to link it with the general term of an arithmetic sequence\u00a0 \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>u<\/mi><mi>n<\/mi><\/msub><mo>=<\/mo><msub><mi>u<\/mi><mn>1<\/mn><\/msub><mo>+<\/mo><mfenced><mrow><mi>n<\/mi><mo>&#8211;<\/mo><mn>1<\/mn><\/mrow><\/mfenced><mi>d<\/mi><\/math>\r\n and draw the conclusion that the coefficient of <em>n <\/em>represents the common difference and also the gradient of the line. Here is an example<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-1725\" src=\"http:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/04\/Capture1.jpg\" alt=\"\" width=\"1542\" height=\"706\" srcset=\"https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/04\/Capture1.jpg 1542w, https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/04\/Capture1-300x137.jpg 300w, https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/04\/Capture1-1024x469.jpg 1024w, https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/04\/Capture1-768x352.jpg 768w, https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/04\/Capture1-1536x703.jpg 1536w, https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/04\/Capture1-1200x549.jpg 1200w\" sizes=\"auto, (max-width: 1542px) 100vw, 1542px\" \/><\/p>\r\n<p>You can sketch exponential functions of the form\u00a0 \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>y<\/mi><mo>=<\/mo><mo>&#160;<\/mo><mi>a<\/mi><mo>&#160;<\/mo><mo>&#215;<\/mo><msup><mi>b<\/mi><mi>n<\/mi><\/msup><\/math>\r\n to understand geometric series.<\/p>\r\n<p>2. Sketch the graph of quadratics of the form\u00a0 \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>y<\/mi><mo>=<\/mo><mi>a<\/mi><msup><mi>n<\/mi><mn>2<\/mn><\/msup><mo>+<\/mo><mi>b<\/mi><mi>n<\/mi><\/math>\r\n to understand the sum to <em>n\u00a0<\/em>terms of an arithmetic series. e.g.<\/p>\r\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-1726\" src=\"http:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/04\/Capture2.jpg\" alt=\"\" width=\"1342\" height=\"659\" srcset=\"https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/04\/Capture2.jpg 1342w, https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/04\/Capture2-300x147.jpg 300w, https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/04\/Capture2-1024x503.jpg 1024w, https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/04\/Capture2-768x377.jpg 768w, https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/04\/Capture2-1200x589.jpg 1200w\" sizes=\"auto, (max-width: 1342px) 100vw, 1342px\" \/><\/p><!-- AddThis Advanced Settings generic via filter on the_content --><!-- AddThis Share Buttons generic via filter on the_content -->","protected":false},"excerpt":{"rendered":"1. To understand the concept of arithmetic sequence sketch the graph of some linear functions using some graphing software ( I used DESMOS). You will observe that when n=1,&#160;2,&#160;3,&#160;&#8230;.. the y-values will change increase\/decrease with a constant number. Try to link it with the general term of an arithmetic sequence\u00a0 un=u1+n&#8211;1d and draw the conclusion [&hellip;]<!-- AddThis Advanced Settings generic via filter on get_the_excerpt --><!-- AddThis Share Buttons generic via filter on get_the_excerpt -->","protected":false},"author":4,"featured_media":0,"comment_status":"closed","ping_status":"closed","template":"","class_list":["post-1724","knowledgebase","type-knowledgebase","status-publish","hentry","knowledgebase_cat-sequence-and-series","no-wpautop"],"_links":{"self":[{"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/knowledgebase\/1724","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/knowledgebase"}],"about":[{"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/types\/knowledgebase"}],"author":[{"embeddable":true,"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/users\/4"}],"replies":[{"embeddable":true,"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/comments?post=1724"}],"version-history":[{"count":2,"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/knowledgebase\/1724\/revisions"}],"predecessor-version":[{"id":1728,"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/knowledgebase\/1724\/revisions\/1728"}],"wp:attachment":[{"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/media?parent=1724"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}