{"id":36620,"date":"2025-06-25T08:20:29","date_gmt":"2025-06-25T08:20:29","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=36620"},"modified":"2025-06-25T08:20:40","modified_gmt":"2025-06-25T08:20:40","slug":"find-the-missing-term-in-this-geometric-sequence","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/find-the-missing-term-in-this-geometric-sequence\/","title":{"rendered":"Find the missing term in this geometric sequence"},"content":{"rendered":"\n<p>Find the missing term in this geometric sequence: 2, [ ? ], 98<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-cyan-blue-color\">The correct answer and explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>The geometric sequence given is: 2, [ ? ], 98.<\/p>\n\n\n\n<p>To find the missing term, we need to understand the properties of a geometric sequence. In a geometric sequence, each term after the first is found by multiplying the previous term by a constant called the common ratio (r).<\/p>\n\n\n\n<p>Let the missing term be xx. The sequence is then:<\/p>\n\n\n\n<p>2,x,982, \\quad x, \\quad 98<\/p>\n\n\n\n<p>The common ratio can be expressed as: r=x2=98xr = \\frac{x}{2} = \\frac{98}{x}<\/p>\n\n\n\n<p>Since the ratio between consecutive terms is constant, these two ratios must be equal: x2=98x\\frac{x}{2} = \\frac{98}{x}<\/p>\n\n\n\n<p>Cross-multiplying gives: x2=2\u00d798x^2 = 2 \\times 98 x2=196x^2 = 196<\/p>\n\n\n\n<p>Taking the square root of both sides: x=\u00b1196=\u00b114x = \\pm \\sqrt{196} = \\pm 14<\/p>\n\n\n\n<p>Thus, the missing term could be either 1414 or \u221214-14.<\/p>\n\n\n\n<p>To verify, check if the sequence forms a geometric progression with each candidate:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>For x=14x = 14, the ratios are 142=7\\frac{14}{2} = 7 and 9814=7\\frac{98}{14} = 7. The common ratio is 7, so the sequence is 2,14,982, 14, 98.<\/li>\n\n\n\n<li>For x=\u221214x = -14, the ratios are \u2212142=\u22127\\frac{-14}{2} = -7 and 98\u221214=\u22127\\frac{98}{-14} = -7. The common ratio is -7, so the sequence is 2,\u221214,982, -14, 98.<\/li>\n<\/ul>\n\n\n\n<p>Both values satisfy the condition of a geometric sequence, so the missing term could be either 1414 or \u221214-14, depending on the context or additional constraints.<\/p>\n\n\n\n<p><strong>Summary:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The missing term xx is found by setting the ratio between terms equal.<\/li>\n\n\n\n<li>Solving x2=98x\\frac{x}{2} = \\frac{98}{x} yields x2=196x^2 = 196.<\/li>\n\n\n\n<li>Taking the square root gives two possible values: 1414 or \u221214-14.<\/li>\n\n\n\n<li>Both values form valid geometric sequences with common ratios of 7 or -7, respectively.<\/li>\n<\/ul>\n\n\n\n<p>Hence, the missing term in the geometric sequence is either <strong>14<\/strong> or <strong>-14<\/strong>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Find the missing term in this geometric sequence: 2, [ ? ], 98 The correct answer and explanation is: The geometric sequence given is: 2, [ ? ], 98. To find the missing term, we need to understand the properties of a geometric sequence. In a geometric sequence, each term after the first is found [&hellip;]<\/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-36620","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/36620","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=36620"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/36620\/revisions"}],"predecessor-version":[{"id":36621,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/36620\/revisions\/36621"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=36620"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=36620"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=36620"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}