{"id":258185,"date":"2025-07-18T02:36:55","date_gmt":"2025-07-18T02:36:55","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=258185"},"modified":"2025-07-18T02:36:58","modified_gmt":"2025-07-18T02:36:58","slug":"evaluate-4","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/18\/evaluate-4\/","title":{"rendered":"Evaluate\u00a0"},"content":{"rendered":"\n
\"\"<\/figure>\n\n\n\n

The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n

The correct answer is 20<\/strong>.<\/p>\n\n\n\n

Explanation<\/h3>\n\n\n\n

The problem asks to evaluate the summation, represented by the Greek letter sigma (\u03a3). The expression is the sum of the terms (20 – 2^n) for integer values of n starting from 2 and ending at 5. To solve this, we will substitute each value of n (2, 3, 4, and 5) into the expression, calculate the result for each term, and then add all of these results together.<\/p>\n\n\n\n

Let’s break down the calculation for each value of n:<\/p>\n\n\n\n

    \n
  1. For n = 2:<\/strong>
    The term is (20 – 2\u00b2).
    2\u00b2 = 4.
    So, the term is (20 – 4) = 16.<\/li>\n\n\n\n
  2. For n = 3:<\/strong>
    The term is (20 – 2\u00b3).
    2\u00b3 = 8.
    So, the term is (20 – 8) = 12.<\/li>\n\n\n\n
  3. For n = 4:<\/strong>
    The term is (20 – 2\u2074).
    2\u2074 = 16.
    So, the term is (20 – 16) = 4.<\/li>\n\n\n\n
  4. For n = 5:<\/strong>
    The term is (20 – 2\u2075).
    2\u2075 = 32.
    So, the term is (20 – 32) = -12.<\/li>\n<\/ol>\n\n\n\n

    Now, we sum these four resulting values:
    Sum = (Value for n=2) + (Value for n=3) + (Value for n=4) + (Value for n=5)
    Sum = 16 + 12 + 4 + (-12)<\/p>\n\n\n\n

    We can simplify the addition. Notice that we have a +12 and a -12, which cancel each other out:
    Sum = 16 + 4 + (12 – 12)
    Sum = 16 + 4 + 0
    Sum = 20<\/p>\n\n\n\n

    Alternatively, we could use the properties of summation. The original expression can be split into two separate sums: the sum of 20 and the sum of 2^n. The number of terms is 5 – 2 + 1 = 4.
    Sum = \u03a3(20) – \u03a3(2^n) from n=2 to 5.
    The first part is (4 \u00d7 20) = 80.
    The second part is (2\u00b2 + 2\u00b3 + 2\u2074 + 2\u2075) = (4 + 8 + 16 + 32) = 60.
    The final result is 80 – 60 = 20. Both methods yield the same answer.<\/p>\n\n\n\n

    \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

    The Correct Answer and Explanation is: The correct answer is 20. Explanation The problem asks to evaluate the summation, represented by the Greek letter sigma (\u03a3). The expression is the sum of the terms (20 – 2^n) for integer values of n starting from 2 and ending at 5. To solve this, we will substitute each […]<\/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-258185","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/258185","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=258185"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/258185\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=258185"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=258185"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=258185"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}