The first 3 terms of a sequence are given. Write your answer as a decimal or hole number round to the nearest thousand twelve seventeen twenty two, find the thirty six term<\/p>\n\n\n\n
The correct answer and explanation is:<\/strong><\/mark><\/p>\n\n\n\n Let’s analyze the sequence given:<\/p>\n\n\n\n Sequence:<\/strong> 12, 17, 22, …<\/p>\n\n\n\n Look at the differences between consecutive terms:<\/p>\n\n\n\n The difference between each term is constant (+5), so this is an arithmetic sequence<\/strong> with:<\/p>\n\n\n\n The nn-th term of an arithmetic sequence is given by: an=a1+(n\u22121)da_n = a_1 + (n – 1)d<\/p>\n\n\n\n Substitute a1=12a_1 = 12, d=5d = 5, and n=36n = 36: a36=12+(36\u22121)\u00d75=12+35\u00d75=12+175=187a_{36} = 12 + (36 – 1) \\times 5 = 12 + 35 \\times 5 = 12 + 175 = 187<\/p>\n\n\n\n 187\\boxed{187}<\/p>\n\n\n\n The sequence provided is 12, 17, 22, and so forth. By examining the difference between consecutive terms, we see a consistent increase of 5 each time: from 12 to 17 is +5, and from 17 to 22 is also +5. This consistent increment means the sequence is arithmetic.<\/p>\n\n\n\n An arithmetic sequence is defined by a starting value (called the first term, a1a_1) and a fixed step size (called the common difference, dd). Here, the first term a1a_1 is 12, and the common difference dd is 5.<\/p>\n\n\n\n To find any term in the sequence, the formula used is: an=a1+(n\u22121)da_n = a_1 + (n – 1)d<\/p>\n\n\n\n where ana_n is the nn-th term, a1a_1 is the first term, and dd is the common difference.<\/p>\n\n\n\n In this problem, we’re asked to find the 36th term. Substituting the known values, we calculate: a36=12+(36\u22121)\u00d75=12+35\u00d75=12+175=187a_{36} = 12 + (36 – 1) \\times 5 = 12 + 35 \\times 5 = 12 + 175 = 187<\/p>\n\n\n\n Thus, the 36th term in the sequence is 187.<\/p>\n\n\n\n Because this value is a whole number, there’s no need to round further. The answer is simply 187<\/strong>.<\/p>\n\n\n\n This approach can be used for any term in the sequence by changing the value of nn, making arithmetic sequences straightforward and predictable. Arithmetic sequences appear in many real-world situations where things increase or decrease by a constant amount regularly.<\/p>\n","protected":false},"excerpt":{"rendered":" The first 3 terms of a sequence are given. Write your answer as a decimal or hole number round to the nearest thousand twelve seventeen twenty two, find the thirty six term The correct answer and explanation is: Let’s analyze the sequence given: Sequence: 12, 17, 22, … Step 1: Identify the pattern Look at […]<\/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-27900","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/27900","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=27900"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/27900\/revisions"}],"predecessor-version":[{"id":27901,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/27900\/revisions\/27901"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=27900"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=27900"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=27900"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
\n\n\n\nStep 1: Identify the pattern<\/h3>\n\n\n\n
\n
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\n\n\n\nStep 2: Find the 36th term formula<\/h3>\n\n\n\n
\n\n\n\nStep 3: Calculate the 36th term<\/h3>\n\n\n\n
\n\n\n\nFinal answer:<\/strong><\/h3>\n\n\n\n
\n\n\n\nExplanation (300 words):<\/h3>\n\n\n\n