{"id":1544,"date":"2024-10-07T13:27:32","date_gmt":"2024-10-07T13:27:32","guid":{"rendered":"https:\/\/loudounmathtutoring.org\/?page_id=1544"},"modified":"2024-10-07T13:34:11","modified_gmt":"2024-10-07T13:34:11","slug":"teaching-aids-sequences-and-series","status":"publish","type":"page","link":"https:\/\/loudounmathtutoring.org\/?page_id=1544","title":{"rendered":"Teaching Aids &#8211; Sequences and Series"},"content":{"rendered":"\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<figure class=\"wp-block-image size-large\"><a href=\"https:\/\/loudounmathtutoring.org\/wp-content\/uploads\/2024\/10\/SummationProperties.png\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"648\" src=\"https:\/\/loudounmathtutoring.org\/wp-content\/uploads\/2024\/10\/SummationProperties-1024x648.png\" alt=\"\" class=\"wp-image-1545\" srcset=\"https:\/\/loudounmathtutoring.org\/wp-content\/uploads\/2024\/10\/SummationProperties-1024x648.png 1024w, https:\/\/loudounmathtutoring.org\/wp-content\/uploads\/2024\/10\/SummationProperties-300x190.png 300w, https:\/\/loudounmathtutoring.org\/wp-content\/uploads\/2024\/10\/SummationProperties-768x486.png 768w, https:\/\/loudounmathtutoring.org\/wp-content\/uploads\/2024\/10\/SummationProperties.png 1177w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/a><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/loudounmathtutoring.org\/wp-content\/uploads\/2024\/10\/SummationFormulas.png\"><img loading=\"lazy\" decoding=\"async\" width=\"520\" height=\"725\" src=\"https:\/\/loudounmathtutoring.org\/wp-content\/uploads\/2024\/10\/SummationFormulas.png\" alt=\"\" class=\"wp-image-1546\" srcset=\"https:\/\/loudounmathtutoring.org\/wp-content\/uploads\/2024\/10\/SummationFormulas.png 520w, https:\/\/loudounmathtutoring.org\/wp-content\/uploads\/2024\/10\/SummationFormulas-215x300.png 215w\" sizes=\"auto, (max-width: 520px) 100vw, 520px\" \/><\/a><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/loudounmathtutoring.org\/wp-content\/uploads\/2024\/10\/yLsqh65kki-pascals-triangle-5.png\"><img loading=\"lazy\" decoding=\"async\" width=\"510\" height=\"396\" src=\"https:\/\/loudounmathtutoring.org\/wp-content\/uploads\/2024\/10\/yLsqh65kki-pascals-triangle-5.png\" alt=\"\" class=\"wp-image-1547\" srcset=\"https:\/\/loudounmathtutoring.org\/wp-content\/uploads\/2024\/10\/yLsqh65kki-pascals-triangle-5.png 510w, https:\/\/loudounmathtutoring.org\/wp-content\/uploads\/2024\/10\/yLsqh65kki-pascals-triangle-5-300x233.png 300w\" sizes=\"auto, (max-width: 510px) 100vw, 510px\" \/><\/a><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/loudounmathtutoring.org\/wp-content\/uploads\/2024\/10\/v4-460px-Calculate-xy^n-with-Pascals-Triangle-Step-3-Version-2.jpg.webp\"><img loading=\"lazy\" decoding=\"async\" width=\"460\" height=\"345\" src=\"https:\/\/loudounmathtutoring.org\/wp-content\/uploads\/2024\/10\/v4-460px-Calculate-xy^n-with-Pascals-Triangle-Step-3-Version-2.jpg.webp\" alt=\"\" class=\"wp-image-1548\" srcset=\"https:\/\/loudounmathtutoring.org\/wp-content\/uploads\/2024\/10\/v4-460px-Calculate-xy^n-with-Pascals-Triangle-Step-3-Version-2.jpg.webp 460w, https:\/\/loudounmathtutoring.org\/wp-content\/uploads\/2024\/10\/v4-460px-Calculate-xy^n-with-Pascals-Triangle-Step-3-Version-2.jpg-300x225.webp 300w\" sizes=\"auto, (max-width: 460px) 100vw, 460px\" \/><\/a><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/loudounmathtutoring.org\/wp-content\/uploads\/2024\/10\/BinomialExpand.jpg\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"768\" src=\"https:\/\/loudounmathtutoring.org\/wp-content\/uploads\/2024\/10\/BinomialExpand.jpg\" alt=\"\" class=\"wp-image-1549\" srcset=\"https:\/\/loudounmathtutoring.org\/wp-content\/uploads\/2024\/10\/BinomialExpand.jpg 1024w, https:\/\/loudounmathtutoring.org\/wp-content\/uploads\/2024\/10\/BinomialExpand-300x225.jpg 300w, https:\/\/loudounmathtutoring.org\/wp-content\/uploads\/2024\/10\/BinomialExpand-768x576.jpg 768w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/a><figcaption class=\"wp-element-caption\">Formula for finding a particular term in expansion of (a + b)n is: Ex.: Find the 4th term in expansion of (a + b)9: This is the 4th term, so value of r (b\u2019s exponent) is 4 \u2013 1 = 3. This means the exponent for a is 9 \u2013 3, or 6. So, we have the variables of the 4th term: a6b3. Coefficient is:<\/figcaption><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<div data-wp-interactive=\"core\/file\" class=\"wp-block-file\"><object data-wp-bind--hidden=\"!state.hasPdfPreview\" hidden class=\"wp-block-file__embed\" data=\"https:\/\/loudounmathtutoring.org\/wp-content\/uploads\/2024\/10\/MAU8B3-Sequences-and-Series-Formula-Sheet.pdf\" type=\"application\/pdf\" style=\"width:100%;height:600px\" aria-label=\"Embed of Sequences and Series Formula Sheet.\"><\/object><a id=\"wp-block-file--media-c9756dc3-8596-4b84-961c-dfc5037bc071\" href=\"https:\/\/loudounmathtutoring.org\/wp-content\/uploads\/2024\/10\/MAU8B3-Sequences-and-Series-Formula-Sheet.pdf\">Sequences and Series Formula Sheet<\/a><a href=\"https:\/\/loudounmathtutoring.org\/wp-content\/uploads\/2024\/10\/MAU8B3-Sequences-and-Series-Formula-Sheet.pdf\" class=\"wp-block-file__button wp-element-button\" download aria-describedby=\"wp-block-file--media-c9756dc3-8596-4b84-961c-dfc5037bc071\">Download<\/a><\/div>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-1544","page","type-page","status-publish","hentry","post"],"_links":{"self":[{"href":"https:\/\/loudounmathtutoring.org\/index.php?rest_route=\/wp\/v2\/pages\/1544","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/loudounmathtutoring.org\/index.php?rest_route=\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/loudounmathtutoring.org\/index.php?rest_route=\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/loudounmathtutoring.org\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/loudounmathtutoring.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1544"}],"version-history":[{"count":2,"href":"https:\/\/loudounmathtutoring.org\/index.php?rest_route=\/wp\/v2\/pages\/1544\/revisions"}],"predecessor-version":[{"id":1553,"href":"https:\/\/loudounmathtutoring.org\/index.php?rest_route=\/wp\/v2\/pages\/1544\/revisions\/1553"}],"wp:attachment":[{"href":"https:\/\/loudounmathtutoring.org\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1544"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}