{"id":277376,"date":"2025-07-31T15:41:30","date_gmt":"2025-07-31T15:41:30","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=277376"},"modified":"2025-07-31T15:41:32","modified_gmt":"2025-07-31T15:41:32","slug":"a-sequence-has-a-common-ratio-of-3-2-and-f581","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/31\/a-sequence-has-a-common-ratio-of-3-2-and-f581\/","title":{"rendered":"A sequence has a common ratio of 3\/2 and f(5)=81.\u00a0"},"content":{"rendered":"\n
\"\"<\/figure>\n\n\n\n

The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n

The correct answer is B. f(x) = 16(3\/2)^(x-1)<\/strong>.<\/p>\n\n\n\n

This problem asks for the explicit formula of a geometric sequence. A geometric sequence is a list of numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio. The standard explicit formula for a geometric sequence is f(x) = a * r^(x-1), where ‘a’ represents the first term of the sequence (f(1)), ‘r’ is the common ratio, and ‘x’ is the term number.<\/p>\n\n\n\n

From the problem statement, we are given two key pieces of information: the common ratio (r) is 3\/2, and the fifth term (f(5)) is 81. Our goal is to use this information to find the first term, ‘a’, and then construct the complete formula.<\/p>\n\n\n\n

We begin by substituting the known values into the general formula. We have x = 5, f(5) = 81, and r = 3\/2. Plugging these into the equation gives us:
81 = a * (3\/2)^(5-1)<\/p>\n\n\n\n

First, we simplify the exponent:
81 = a * (3\/2)^4<\/p>\n\n\n\n

Next, we calculate the value of (3\/2) raised to the fourth power. This involves raising both the numerator and the denominator to the power of 4:
(3\/2)^4 = 3^4 \/ 2^4 = 81 \/ 16<\/p>\n\n\n\n

Now we substitute this value back into our equation:
81 = a * (81 \/ 16)<\/p>\n\n\n\n

To solve for ‘a’, we need to isolate it. We can do this by dividing both sides of the equation by (81\/16). Dividing by a fraction is the same as multiplying by its reciprocal, which is (16\/81).
a = 81 * (16 \/ 81)
a = 16<\/p>\n\n\n\n

Now that we have found the first term, a = 16, we can write the final explicit formula by substituting the values of ‘a’ and ‘r’ back into the general form:
f(x) = 16 * (3\/2)^(x-1)<\/p>\n\n\n\n

Comparing this result with the given choices, it perfectly matches option B. We can also verify this answer by plugging x = 5 back into our derived formula to ensure it yields the correct value of 81, which it does.<\/p>\n\n\n\n

\"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

The Correct Answer and Explanation is: The correct answer is B. f(x) = 16(3\/2)^(x-1). This problem asks for the explicit formula of a geometric sequence. A geometric sequence is a list of numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio. The […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-277376","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/277376","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=277376"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/277376\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=277376"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=277376"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=277376"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}