{"id":17933,"date":"2026-05-02T20:11:33","date_gmt":"2026-05-02T14:11:33","guid":{"rendered":"https:\/\/mcqacademy.com\/en\/mcq\/arithmetic-progression-calculation-14\/"},"modified":"2026-05-02T20:11:33","modified_gmt":"2026-05-02T14:11:33","slug":"arithmetic-progression-calculation-14","status":"publish","type":"mcq","link":"https:\/\/mcqacademy.com\/en\/mcq\/arithmetic-progression-calculation-14\/","title":{"rendered":"Arithmetic Progression Calculation 14"},"content":{"rendered":"<p>In an arithmetic progression, first term a=13 and common difference d=-4. Find the sum of the first 9 terms.<\/p>\n\n<ul class=\"quiz-options wp-block-list\">\n<li>-31<\/li>\n<li>27<\/li>\n<li>-40<\/li>\n<li>-27<\/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-17933","mcq","type-mcq","status-publish","hentry","topic-algebra","topic-sequences-and-series","subject-mathematics","education_level-hsc"],"mcq_note":"For an arithmetic progression, do not add all the terms one by one; use the AP sum formula. First identify the first term a, the common difference d, and the number of terms n. The sum is S_n=n\/2[2a+(n-1)d]. Thus S_9=9\/2[2(13)+(9-1)(-4)]=-27. So the required sum is obtained directly from the formula after substitution.","mcq_options":[{"right":"no","answer":"-31"},{"right":"no","answer":"27"},{"right":"no","answer":"-40"},{"right":"yes","answer":"-27"}],"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\/17933","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=17933"}],"wp:attachment":[{"href":"https:\/\/mcqacademy.com\/en\/wp-json\/wp\/v2\/media?parent=17933"}],"wp:term":[{"taxonomy":"topic","embeddable":true,"href":"https:\/\/mcqacademy.com\/en\/wp-json\/wp\/v2\/topic?post=17933"},{"taxonomy":"subject","embeddable":true,"href":"https:\/\/mcqacademy.com\/en\/wp-json\/wp\/v2\/subject?post=17933"},{"taxonomy":"education_level","embeddable":true,"href":"https:\/\/mcqacademy.com\/en\/wp-json\/wp\/v2\/education_level?post=17933"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}