{"id":214735,"date":"2025-05-15T10:07:32","date_gmt":"2025-05-15T10:07:32","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=214735"},"modified":"2025-05-15T10:07:34","modified_gmt":"2025-05-15T10:07:34","slug":"which-expression-is-equivalent-to-the-given-expression-2","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/05\/15\/which-expression-is-equivalent-to-the-given-expression-2\/","title":{"rendered":"Which expression is equivalent to the given expression"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">Which expression is equivalent to the given expression? 6 (2i \u2013 3) i=-3<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">YOUR ANSWER CORRECT ANSWER<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">5 (2i \u2013 3) i=-2<br>5 9+ (2\u20133) i=-2<br>9+ (2i \u2013 3) i=-2<br>5<br>5 -9+ (2i \u2013 3) ) i=-3<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-1-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Let&#8217;s carefully analyze the problem you gave:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Original expression:<\/strong><br>$6 \\sum_{i=-3}^{?} (2i &#8211; 3)$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">But the problem statement seems a bit jumbled or incomplete \u2014 it shows:<br><code>6 (2i \u2013 3) i=-3<\/code><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">This looks like a summation notation issue or missing parts. Based on the options, it seems like the question wants to know which expression is equivalent to the original summation:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$$<br>6 \\sum_{i=-3}^{something} (2i &#8211; 3)<br>$$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">and the options involve expressions like:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>$5 \\sum_{i=-2} (2i &#8211; 3)$<\/li>\n\n\n\n<li>$5 \\sum_{i=-2} 9 + (2 &#8211; 3)$<\/li>\n\n\n\n<li>$\\sum_{i=-2} 9 + (2i &#8211; 3)$<\/li>\n\n\n\n<li>$5$<\/li>\n\n\n\n<li>$5 \\sum_{i=-3} -9 + (2i &#8211; 3)$<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Step 1: Clarify the original expression<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Let&#8217;s assume the original expression is:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$$<br>6 \\sum_{i=-3}^{n} (2i &#8211; 3)<br>$$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">for some $n$, and we want to find an equivalent expression.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 2: Understand the summation of $2i &#8211; 3$<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">The sum from $i = a$ to $i = b$ of $2i &#8211; 3$ can be computed as:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$$<br>\\sum_{i=a}^b (2i &#8211; 3) = 2 \\sum_{i=a}^b i &#8211; 3 \\sum_{i=a}^b 1 = 2 \\left(\\frac{(b+a)(b &#8211; a + 1)}{2}\\right) &#8211; 3 (b &#8211; a + 1)<br>$$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Here:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>$\\sum_{i=a}^b i = \\frac{(b+a)(b &#8211; a + 1)}{2}$ is the formula for the sum of an arithmetic series.<\/li>\n\n\n\n<li>$\\sum_{i=a}^b 1 = (b &#8211; a + 1)$ is the number of terms.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Step 3: Apply this for given limits<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">For example, if we consider the sum from $i = -3$ to $i = -3$ (only one term), then:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$$<br>\\sum_{i=-3}^{-3} (2i &#8211; 3) = 2(-3) &#8211; 3 = -6 &#8211; 3 = -9<br>$$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">If the sum goes from $i = -3$ to $i = -2$ (two terms):<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$$<br>\\sum_{i=-3}^{-2} (2i &#8211; 3) = (2(-3) &#8211; 3) + (2(-2) &#8211; 3) = (-6 &#8211; 3) + (-4 &#8211; 3) = -9 + (-7) = -16<br>$$<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 4: Compare the given options<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The option $5 \\sum_{i=-2} (2i &#8211; 3)$ is incomplete (sum to what?).<\/li>\n\n\n\n<li>Another option shows $9 + (2 &#8211; 3)$, which looks unrelated.<\/li>\n\n\n\n<li>$\\sum_{i=-2} 9 + (2i &#8211; 3)$ is not standard notation.<\/li>\n\n\n\n<li>$5$ alone is a number, unlikely equivalent to a sum expression.<\/li>\n\n\n\n<li>$5 \\sum_{i=-3} -9 + (2i &#8211; 3)$ again is ambiguous.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Step 5: Make sense of the problem<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">If the original expression is:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$$<br>6 \\sum_{i=-3}^{-3} (2i &#8211; 3)<br>$$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">which equals<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$$<br>6 \\times (-9) = -54<br>$$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">And if we consider<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$$<br>5 \\sum_{i=-2}^{-2} (2i &#8211; 3)<br>$$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">this equals:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$$<br>5 \\times (2(-2) &#8211; 3) = 5 \\times (-4 &#8211; 3) = 5 \\times (-7) = -35<br>$$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">This is <strong>not equal<\/strong> to the original value.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Conclusion:<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">The original question is ambiguous because of missing limits or summation signs.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">If I had to guess the intended question:<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">&#8220;Which expression is equivalent to $6 \\sum_{i=-3}^k (2i &#8211; 3)$ for some $k$?&#8221; and the correct answer involves shifting the index or adjusting the multiplier.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\">Explanation of Equivalent Summation Expressions (300+ words):<\/h1>\n\n\n\n<p class=\"wp-block-paragraph\">Summation expressions can sometimes be rewritten in different but equivalent forms by changing the index of summation or adjusting the constant multipliers outside the summation.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">For example, the summation<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$$<br>\\sum_{i=a}^b f(i)<br>$$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">means adding the values of $f(i)$ starting at $i = a$ up to $i = b$. If we multiply the entire summation by a constant $c$, it\u2019s the same as:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$$<br>c \\sum_{i=a}^b f(i) = \\sum_{i=a}^b c \\times f(i)<br>$$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Also, sometimes, the index of summation $i$ can be shifted by an integer $m$ to rewrite the sum, such as:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$$<br>\\sum_{i=a}^b f(i) = \\sum_{j = a + m}^{b + m} f(j &#8211; m)<br>$$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">where $j = i + m$. This change can simplify calculations or match given expressions.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">In your problem, the expression involves $6 \\sum (2i &#8211; 3)$, which could be rewritten with a different index starting at $i = -2$ instead of $i = -3$, but then the multiplier and limits would adjust accordingly to keep the sum equivalent.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">When trying to find an equivalent expression, you need<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Which expression is equivalent to the given expression? 6 (2i \u2013 3) i=-3 YOUR ANSWER CORRECT ANSWER 5 (2i \u2013 3) i=-25 9+ (2\u20133) i=-29+ (2i \u2013 3) i=-255 -9+ (2i \u2013 3) ) i=-3 The Correct Answer and Explanation is: Let&#8217;s carefully analyze the problem you gave: Original expression:$6 \\sum_{i=-3}^{?} (2i &#8211; 3)$ But [&hellip;]<\/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-214735","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/214735","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=214735"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/214735\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=214735"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=214735"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=214735"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}