what are the four arithmetic mean between 8 and 18 solution po show solution<\/p>\n\n\n\n
The correct answer and explanation is:<\/strong><\/mark><\/p>\n\n\n\n To find the four arithmetic means between 8 and 18<\/strong>, we are essentially inserting four numbers<\/strong> between 8 and 18 such that the entire sequence forms an arithmetic sequence<\/strong> (a sequence with a constant difference between each term).<\/p>\n\n\n\n We want to find four arithmetic means between 8 and 18.<\/p>\n\n\n\n That means the sequence will have: Let\u2019s denote this arithmetic sequence as: Where:<\/p>\n\n\n\n an=a1+(n\u22121)\u22c5da_n = a_1 + (n – 1) \\cdot d<\/p>\n\n\n\n We know: a6=8+(6\u22121)d=18a_6 = 8 + (6 – 1)d = 18 8+5d=188 + 5d = 18 5d=105d = 10 d=2d = 2<\/p>\n\n\n\n Now that we know the common difference is 2:<\/p>\n\n\n\n The four arithmetic means between 8 and 18 are: In mathematics, an arithmetic sequence is a sequence of numbers in which the difference between any two consecutive terms is constant. This difference is called the common difference (d)<\/em>.<\/p>\n\n\n\n To find multiple arithmetic means between two numbers, we essentially construct a longer arithmetic sequence that starts with the first number and ends with the last, and the terms in between are the arithmetic means we\u2019re looking for.<\/p>\n\n\n\n In this case, we need four arithmetic means<\/strong> between 8 and 18. This means our full sequence must have six terms<\/strong> in total (including the given first and last terms).<\/p>\n\n\n\n We use the arithmetic formula for the nth term: an=a1+(n\u22121)da_n = a_1 + (n – 1)d<\/p>\n\n\n\n By plugging in the values (with a\u2086 = 18 and a\u2081 = 8), we can solve for the common difference, which turns out to be 2.<\/p>\n\n\n\n Then, using this common difference, we calculate the four missing values between 8 and 18 by repeatedly adding 2. This gives us 10, 12, 14, and 16 as the four arithmetic means.<\/p>\n\n\n\n This approach ensures the sequence increases uniformly, maintaining the essential property of an arithmetic sequence.<\/p>\n","protected":false},"excerpt":{"rendered":" what are the four arithmetic mean between 8 and 18 solution po show solution The correct answer and explanation is: To find the four arithmetic means between 8 and 18, we are essentially inserting four numbers between 8 and 18 such that the entire sequence forms an arithmetic sequence (a sequence with a constant difference […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-21590","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/21590","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/comments?post=21590"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/21590\/revisions"}],"predecessor-version":[{"id":21591,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/21590\/revisions\/21591"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=21590"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=21590"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=21590"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
\n\n\n\n\u2705 Step-by-Step Solution:<\/strong><\/h3>\n\n\n\n
8, ___, ___, ___, ___, 18<\/strong>
This is a total of 6 terms<\/strong>.<\/p>\n\n\n\n
a\u2081, a\u2082, a\u2083, a\u2084, a\u2085, a\u2086<\/strong><\/p>\n\n\n\n\n
\n\n\n\n\ud83d\udc49 Step 1: Use the formula for the nth term of an arithmetic sequence:<\/h3>\n\n\n\n
\n\n\n\n\ud83d\udc49 Step 2: Use the common difference to find the missing terms:<\/h3>\n\n\n\n
\n
\n\n\n\n\u2705 Final Answer:<\/h3>\n\n\n\n
10, 12, 14, 16<\/strong><\/p>\n\n\n\n
\n\n\n\n\ud83e\udde0 300-Word Explanation:<\/h3>\n\n\n\n