{"id":17953,"date":"2026-05-02T20:15:25","date_gmt":"2026-05-02T14:15:25","guid":{"rendered":"https:\/\/mcqacademy.com\/en\/mcq\/geometric-progression-calculation-14\/"},"modified":"2026-05-02T20:15:25","modified_gmt":"2026-05-02T14:15:25","slug":"geometric-progression-calculation-14","status":"publish","type":"mcq","link":"https:\/\/mcqacademy.com\/en\/mcq\/geometric-progression-calculation-14\/","title":{"rendered":"Geometric Progression Calculation 14"},"content":{"rendered":"<p>For a geometric progression with first term 5 and common ratio 1\/2, find the sum of the first 8 terms.<\/p>\n\n<ul class=\"quiz-options wp-block-list\">\n<li>1403\/128<\/li>\n<li>1275\/128<\/li>\n<li>1275\/64<\/li>\n<li>-1275\/128<\/li>\n<\/ul>\n","protected":false},"author":39,"featured_media":0,"comment_status":"open","ping_status":"closed","template":"","topic":[2705,2599],"subject":[1425],"education_level":[1896],"class_list":["post-17953","mcq","type-mcq","status-publish","hentry","topic-algebra","topic-sequences-and-series","subject-mathematics","education_level-hsc"],"mcq_note":"For a geometric progression, each term is multiplied by the same common ratio. Since this question asks for a sum, use the finite GP sum formula rather than adding terms manually. For r\u22601, S_n=a(r^n-1)\/(r-1). Hence S_8=5((1\/2)^8-1)\/(1\/2-1)=1275\/128. Keep the sign of the first term and the ratio carefully, because they control whether the sum is positive or negative.","mcq_options":[{"right":"no","answer":"1403\/128"},{"right":"yes","answer":"1275\/128"},{"right":"no","answer":"1275\/64"},{"right":"no","answer":"-1275\/128"}],"multi_answers":"no","subject_terms":[{"id":1425,"title":"Mathematics","slug":"mathematics"}],"topic_terms":[{"id":2705,"title":"Algebra","slug":"algebra"},{"id":2599,"title":"Sequences And Series","slug":"sequences-and-series"}],"_links":{"self":[{"href":"https:\/\/mcqacademy.com\/en\/wp-json\/wp\/v2\/mcq\/17953","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mcqacademy.com\/en\/wp-json\/wp\/v2\/mcq"}],"about":[{"href":"https:\/\/mcqacademy.com\/en\/wp-json\/wp\/v2\/types\/mcq"}],"author":[{"embeddable":true,"href":"https:\/\/mcqacademy.com\/en\/wp-json\/wp\/v2\/users\/39"}],"replies":[{"embeddable":true,"href":"https:\/\/mcqacademy.com\/en\/wp-json\/wp\/v2\/comments?post=17953"}],"wp:attachment":[{"href":"https:\/\/mcqacademy.com\/en\/wp-json\/wp\/v2\/media?parent=17953"}],"wp:term":[{"taxonomy":"topic","embeddable":true,"href":"https:\/\/mcqacademy.com\/en\/wp-json\/wp\/v2\/topic?post=17953"},{"taxonomy":"subject","embeddable":true,"href":"https:\/\/mcqacademy.com\/en\/wp-json\/wp\/v2\/subject?post=17953"},{"taxonomy":"education_level","embeddable":true,"href":"https:\/\/mcqacademy.com\/en\/wp-json\/wp\/v2\/education_level?post=17953"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}