{"id":25984,"date":"2025-06-19T08:50:59","date_gmt":"2025-06-19T08:50:59","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=25984"},"modified":"2025-06-19T08:51:00","modified_gmt":"2025-06-19T08:51:00","slug":"the-next-two-terms-of-the-given-sequence-1-3-7-15-31","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/the-next-two-terms-of-the-given-sequence-1-3-7-15-31\/","title":{"rendered":"The next two terms of the given sequence 1 3 7 15 31"},"content":{"rendered":"\n<p>The next two terms of the given sequence 1 3 7 15 31<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-green-cyan-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p><strong>Correct Answer:<\/strong><br>The next two terms in the sequence <strong>1, 3, 7, 15, 31<\/strong> are <strong>63<\/strong> and <strong>127<\/strong>.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p><strong>Explanation:<\/strong><\/p>\n\n\n\n<p>To identify the next terms in a number sequence, we look for a pattern in how the terms change from one to the next.<\/p>\n\n\n\n<p>Let us examine the given sequence:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>1<\/li>\n\n\n\n<li>3<\/li>\n\n\n\n<li>7<\/li>\n\n\n\n<li>15<\/li>\n\n\n\n<li>31<\/li>\n<\/ul>\n\n\n\n<p>We can look at the difference between each pair of consecutive terms:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>3 \u2212 1 = 2<\/li>\n\n\n\n<li>7 \u2212 3 = 4<\/li>\n\n\n\n<li>15 \u2212 7 = 8<\/li>\n\n\n\n<li>31 \u2212 15 = 16<\/li>\n<\/ul>\n\n\n\n<p>Now observe that the differences are:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>2 = 2\u00b9<\/li>\n\n\n\n<li>4 = 2\u00b2<\/li>\n\n\n\n<li>8 = 2\u00b3<\/li>\n\n\n\n<li>16 = 2\u2074<\/li>\n<\/ul>\n\n\n\n<p>This tells us that each term is formed by adding the next power of 2 to the previous term.<\/p>\n\n\n\n<p>So to find the next number:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Next difference should be 2\u2075 = 32<\/li>\n\n\n\n<li>31 + 32 = <strong>63<\/strong><\/li>\n<\/ul>\n\n\n\n<p>Then:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Next difference should be 2\u2076 = 64<\/li>\n\n\n\n<li>63 + 64 = <strong>127<\/strong><\/li>\n<\/ul>\n\n\n\n<p>So the complete sequence now becomes:<\/p>\n\n\n\n<p><strong>1, 3, 7, 15, 31, 63, 127<\/strong><\/p>\n\n\n\n<p>This is a classic pattern where each term follows the formula:<\/p>\n\n\n\n<p><strong>a\u2099 = 2\u207f \u2212 1<\/strong><\/p>\n\n\n\n<p>Let\u2019s confirm that:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>a\u2081 = 2\u00b9 \u2212 1 = 1<\/li>\n\n\n\n<li>a\u2082 = 2\u00b2 \u2212 1 = 3<\/li>\n\n\n\n<li>a\u2083 = 2\u00b3 \u2212 1 = 7<\/li>\n\n\n\n<li>a\u2084 = 2\u2074 \u2212 1 = 15<\/li>\n\n\n\n<li>a\u2085 = 2\u2075 \u2212 1 = 31<\/li>\n\n\n\n<li>a\u2086 = 2\u2076 \u2212 1 = 63<\/li>\n\n\n\n<li>a\u2087 = 2\u2077 \u2212 1 = 127<\/li>\n<\/ul>\n\n\n\n<p>This shows that the sequence is built by subtracting one from successive powers of two. The pattern is consistent and predictable.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"722\" height=\"1024\" src=\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner10-31.jpeg\" alt=\"\" class=\"wp-image-25985\" srcset=\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner10-31.jpeg 722w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner10-31-212x300.jpeg 212w\" sizes=\"auto, (max-width: 722px) 100vw, 722px\" \/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>The next two terms of the given sequence 1 3 7 15 31 The Correct Answer and Explanation is: Correct Answer:The next two terms in the sequence 1, 3, 7, 15, 31 are 63 and 127. Explanation: To identify the next terms in a number sequence, we look for a pattern in how the terms [&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-25984","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/25984","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=25984"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/25984\/revisions"}],"predecessor-version":[{"id":25986,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/25984\/revisions\/25986"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=25984"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=25984"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=25984"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}