To find the nth term<\/strong> of a geometric sequence<\/strong>, we use the formula:an=a\u22c5rn\u22121a_n = a \\cdot r^{n-1}an\u200b=a\u22c5rn\u22121<\/p>\n\n\n\n Where:<\/p>\n\n\n\n From the given sequence:\u22122, 6, \u221218, 54, \u2212162, \u2026-2,\\ 6,\\ -18,\\ 54,\\ -162,\\ \\ldots\u22122, 6, \u221218, 54, \u2212162, \u2026<\/p>\n\n\n\n r=6\u22122=\u22123r = \\frac{6}{-2} = -3r=\u221226\u200b=\u22123<\/p>\n\n\n\n So each term is multiplied by -3 to get the next one.<\/p>\n\n\n\n Now substitute into the geometric sequence formula:an=\u22122\u22c5(\u22123)n\u22121a_n = -2 \\cdot (-3)^{n-1}an\u200b=\u22122\u22c5(\u22123)n\u22121<\/p>\n\n\n\n an=\u22122(\u22123)n\u22121\\boxed{a_n = -2(-3)^{n-1}}an\u200b=\u22122(\u22123)n\u22121\u200b<\/p>\n\n\n\n A geometric sequence is a list of numbers where each term after the first is found by multiplying the previous one by a fixed number known as the common ratio. In this problem, we are given a sequence: -2, 6, -18, 54, -162. To find a formula that represents the nth term<\/strong> of this sequence, we begin by identifying key components.<\/p>\n\n\n\n The first term<\/strong> is simply the starting number of the sequence, which is -2. This value is referred to as aaa in the general formula.<\/p>\n\n\n\n The common ratio<\/strong> is calculated by dividing any term by the one that comes before it. For instance, 6 divided by -2 gives -3. Repeating this with other terms confirms the ratio is consistent: -18 divided by 6 also equals -3, and so on. This confirms the sequence is indeed geometric, and the common ratio rrr is -3.<\/p>\n\n\n\n Using the geometric formula an=a\u22c5rn\u22121a_n = a \\cdot r^{n-1}an\u200b=a\u22c5rn\u22121, we substitute the known values. This gives us an=\u22122\u22c5(\u22123)n\u22121a_n = -2 \\cdot (-3)^{n-1}an\u200b=\u22122\u22c5(\u22123)n\u22121. This expression will correctly generate every term in the sequence. For example, for n=1n = 1n=1, a1=\u22122\u22c5(\u22123)0=\u22122a_1 = -2 \\cdot (-3)^0 = -2a1\u200b=\u22122\u22c5(\u22123)0=\u22122. For n=2n = 2n=2, a2=\u22122\u22c5(\u22123)1=6a_2 = -2 \\cdot (-3)^1 = 6a2\u200b=\u22122\u22c5(\u22123)1=6, and so on.<\/p>\n\n\n\n This formula is useful because it lets you find any term in the sequence without listing all the terms before it.<\/p>\n\n\n\n Find the nth term of the geometric sequence: -2, ~6_ -18- -54 ~162 The Correct Answer and Explanation is: To find the nth term of a geometric sequence, we use the formula:an=a\u22c5rn\u22121a_n = a \\cdot r^{n-1}an\u200b=a\u22c5rn\u22121 Where: Step 1: Identify the first term and common ratio From the given sequence:\u22122, 6, \u221218, 54, \u2212162, \u2026-2,\\ 6,\\ -18,\\ 54,\\ -162,\\ \\ldots\u22122, 6, \u221218, 54, \u2212162, \u2026 […]<\/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-237496","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/237496","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=237496"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/237496\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=237496"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=237496"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=237496"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}\n
Step 1: Identify the first term and common ratio<\/h3>\n\n\n\n
\n
Step 2: Plug into the formula<\/h3>\n\n\n\n
Final Answer:<\/h3>\n\n\n\n
\n\n\n\nExplanation (300 words):<\/h3>\n\n\n\n
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