{"id":6788,"date":"2014-03-07T16:25:15","date_gmt":"2014-03-07T16:25:15","guid":{"rendered":"https:\/\/schooltutoring.com\/scholarship\/?p=6788"},"modified":"2014-12-02T08:25:31","modified_gmt":"2014-12-02T08:25:31","slug":"math-introduction-to-solving-number-patterns","status":"publish","type":"post","link":"https:\/\/schooltutoring.com\/scholarship\/2014\/03\/07\/math-introduction-to-solving-number-patterns\/","title":{"rendered":"Math Introduction to Solving Number Patterns"},"content":{"rendered":"

Overview:<\/strong><\/p>\n

One problem-solving strategy in mathematics is to look for a pattern that will predict the next number in a sequence.\u00a0 That is often the first step to writing an equation that describes how to find each number.\u00a0 Some famous patterns, such as Fibonacci numbers and Pascal\u2019s triangle, play an important role in number theory.<\/p>\n

What Are Arithmetic Patterns?<\/strong><\/p>\n

Arithmetic patterns are those patterns that can be predicted by adding a constant number to each number in the sequence.\u00a0 The sequence that begins {1, 2, 3, 4, 5\u2026}, the natural numbers, is generated by adding 1 to each number.\u00a0 Similarly the pattern that begins {2, 4, 6, 8\u2026} and the one that begins {1, 3, 5, 7\u2026} are generated by adding 2 to each number.\u00a0 Those simple patterns follow an arithmetic sequence.\u00a0 Similarly, the pattern that begins {3, 7, 11, 15 \u2026} is generated by adding 4 to each number.<\/p>\n

What Are Geometric Patterns?<\/strong><\/p>\n

Geometric patterns can be predicted by multiplying each number in the sequence by a constant.\u00a0 For example, the sequence that begins {5, 10, 20, 40\u2026} is generated by multiplying each number by 2.\u00a0 Similarly, the sequence that begins {4, 2, 1, 0.5, 0.25\u2026} is generated by multiplying each number by \u00bd (or dividing by 2).<\/p>\n

What Are Mixed Patterns?<\/strong><\/p>\n

Some number patterns can combine arithmetic and geometric sequences, or follow other rules entirely. Suppose the sequence is {1, 3, 6, 8, 16\u2026}.\u00a0 The next number in the sequence is 18, and the one following that is 36.\u00a0 That is because 1 + 2 is 3, times 2 is 6, + 2 is 8, times 2 is 16, + 2 is 18, times 2 is 36.\u00a0 Similarly, a pattern such as\u00a0 {1, 3, 3, 5, 3, 7, 3\u2026} is 1 + 2, repeat 3, 3 + 2, repeat 3, 5 + 2, repeat 3, and so on, so that the next numbers in the series would be 9, 3.<\/p>\n

What Are Some Special Patterns?<\/strong><\/p>\n

The Fibonacci numbers are a special pattern.\u00a0 They are in the sequence {0, 1, 1, 2, 3, 5, 8, 13, 21\u2026}, and have properties of their own.\u00a0 Prime numbers are in the pattern {1, 2, 3, 5, 7, 11, 13\u2026}.\u00a0 The pattern {1, 4, 9, 16, 25, 36\u2026} are the squares.<\/p>\n

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Overview: One problem-solving strategy in mathematics is to look for a pattern that will predict the next number in a sequence.\u00a0 That is often the first step to writing an equation that describes how to find each number.\u00a0 Some famous patterns, such as Fibonacci numbers and Pascal\u2019s triangle, play an important role in number theory. […]<\/p>\n","protected":false},"author":22,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"inline_featured_image":false,"footnotes":""},"categories":[2],"tags":[2631,2633,2632],"class_list":["post-6788","post","type-post","status-publish","format-standard","hentry","category-algebra","tag-arithmetic-patterns","tag-fibonacci-numbers","tag-geometric-patterns"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/6788","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/users\/22"}],"replies":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/comments?post=6788"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/6788\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/media?parent=6788"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/categories?post=6788"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/tags?post=6788"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}