{"id":47,"date":"2016-08-05T22:39:26","date_gmt":"2016-08-05T17:09:26","guid":{"rendered":"http:\/\/www.examcoaching.in\/blog\/?p=47"},"modified":"2016-08-06T19:59:11","modified_gmt":"2016-08-06T14:29:11","slug":"sum-of-numbers","status":"publish","type":"post","link":"http:\/\/www.examcoaching.in\/blog\/47\/sum-of-numbers","title":{"rendered":"Sum of Numbers"},"content":{"rendered":"

Sum of First n odd Numbers<\/h2>\n

Sum of First n odd Numbers \u00a0= N2<\/sup><\/p><\/blockquote>\n

Where N\u00a0= (max no + 1)\/2<\/p>\n

Q1: What is the sum of first 5 odd numbers?<\/p>\n

N = 5;
\nSo the numbers are \u00a01, 3, 5, 7, 9
\nSo N2<\/sup> \u00a0= 52<\/sup> = 25
\ni.e. 1+3+5+7+9 = 25<\/p>\n

Q2: What is the sum of first 6\u00a0odd numbers?<\/p>\n

N = 6;
\nSo N2<\/sup> \u00a0= 62<\/sup> =\u00a036<\/p>\n

Q3: What is the sum of first 60 odd numbers?<\/p>\n

N = 60;
\nSo N2<\/sup> \u00a0= 602<\/sup> =\u00a03600<\/p>\n

Q4: Find the sum of all odd numbers from 1 to 25?<\/p>\n

Now the max number giver here is 25
\nSo N \u00a0\u00a0= (max no + 1)\/2 = (25+1)\/2 = 13
\nSo N2<\/sup> \u00a0= 132<\/sup> =\u00a0169<\/p>\n

Sum of First n even\u00a0Numbers<\/h2>\n

Sum of First n odd Numbers \u00a0= N2\u00a0<\/sup> + N
\n= N(N+1)<\/p><\/blockquote>\n

Where N\u00a0= (max no)\/2
\nQ1: What is the sum of first 5 even numbers?<\/p>\n

N = 5;
\nSo the numbers are \u00a02, 4, 6, 8,\u00a010
\nSo N2<\/sup>\u00a0+ N = 52<\/sup>\u00a0+ 5 = 25+5 = 30
\ni.e. 2+4+6+8+10 =\u00a030<\/p>\n

Q2: What is the sum of first 6\u00a0even numbers?<\/p>\n

N = 6;
\nSo N2<\/sup>\u00a0+N = 62<\/sup>\u00a0+6=\u00a036+6 = 42<\/p>\n

Q3: What is the sum of first 45\u00a0even numbers?<\/p>\n

N = 45;
\nSo N2<\/sup>\u00a0+N = 452<\/sup>\u00a0+\u00a045=\u00a02070<\/p>\n

Q4: Find the sum of all odd numbers from 1 to 10?<\/p>\n

Now the max number giver here is 25
\nSo N \u00a0\u00a0= (max no)\/2 = (10)\/2 =\u00a05
\nSo N2<\/sup>\u00a0 + N = 52<\/sup>\u00a0+ 5 =\u00a030<\/p>\n

Sum of First n Natural\u00a0Numbers<\/h2>\n

Sum of First N Natural Numbers\u00a0 = (N2\u00a0<\/sup> + N)\/2
\n= (N * (N+1))\/2<\/p><\/blockquote>\n

Where N is the last Number<\/p>\n

Q1: What is the sum of first 5 natural\u00a0numbers?<\/p>\n

N = 5;
\nSo the numbers are \u00a01, 2, 3, 4,\u00a05
\nSo (N2<\/sup>\u00a0+ N)\/2 = (52<\/sup>\u00a0+ 5)\/2 = (25+5)\/2 = 30\/2 = 15
\ni.e. 1+2+3+4+5 =\u00a015<\/p>\n

Q2: What is the sum of first 10\u00a0even numbers?<\/p>\n

N = 10;
\nSo (N2<\/sup>\u00a0+N)\/2 = (102<\/sup>\u00a0+ 10)\/2 = (100+10)\/2 = 110\/2 =\u00a055<\/p>\n

Q3: What is the sum of Numbers from 1 to 100?<\/p>\n

N = 100;
\nSo (N2<\/sup>\u00a0+N)\/2 = (1002<\/sup>\u00a0+ 100)\/2 = (10000+100)\/2 = 10100\/2 =\u00a05050<\/p>\n

Sum of First n\u00a0Cube<\/h2>\n

Sum of First N Cubes\u00a0 = ((N2\u00a0<\/sup> + N)\/2)2\u00a0<\/sup>
\n= ((N * (N+1))\/2)2\u00a0<\/sup><\/p><\/blockquote>\n

Q1: What is the sum of cubes of first 3\u00a0natural\u00a0numbers?<\/p>\n

N = 3;
\nSo the numbers are \u00a01, 2, 3,\u00a0\u00a0and their cubes are 1, 8, 27 respectively
\nSo ((N2<\/sup>\u00a0+ N)\/2)2<\/sup> = ((32<\/sup>\u00a0+ 3)\/2)2<\/sup> = ((9+3)\/2)2<\/sup> = (12\/2)2<\/sup> =\u00a062<\/sup> = 36<\/p>\n

Q2: What is the sum of first 20 cubes?<\/p>\n

N = 20;
\nSo ((N2<\/sup>\u00a0+ N)\/2)2<\/sup> = ((202<\/sup>\u00a0+ 20)\/2)2<\/sup> = ((400+20)\/2)2<\/sup> = (420\/2)2<\/sup> =\u00a02102<\/sup> =\u00a044100<\/p>\n

Sum of First n\u00a0Squares<\/h2>\n

Sum of First N Squares\u00a0 = ((N2\u00a0<\/sup> + N)*(2N+1))\/6<\/p><\/blockquote>\n

Q1: What is the sum of squares\u00a0of first 20\u00a0natural\u00a0numbers?<\/p>\n

((N2\u00a0<\/sup> + N)*(2N+1))\/6
\n=((202<\/sup>+20)*(2*20+1))\/6
\n=(400+20)*(40+1)\/6
\n=2670<\/p>\n

Q2: Find the sum of 12<\/sup>+22<\/sup>+32<\/sup>+…….+302<\/sup>?<\/p>\n

((N2\u00a0<\/sup> + N)*(2N+1))\/6
\n=((9002<\/sup>+30)*(2*30+1))\/6
\n=(930*61)\/6
\n=9455<\/p>\n","protected":false},"excerpt":{"rendered":"

Sum of First n odd Numbers Sum of First n odd Numbers \u00a0= N2 Where N\u00a0= (max no + 1)\/2 Q1: What is the sum of first 5 odd numbers? N = 5; So the numbers are \u00a01, 3, 5, 7, 9 So N2 \u00a0= 52 = 25 i.e. 1+3+5+7+9 = 25 Q2: What is […]<\/p>\n","protected":false},"author":1,"featured_media":54,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"jetpack_post_was_ever_published":false,"_jetpack_newsletter_access":"","footnotes":"","jetpack_publicize_message":"","jetpack_is_tweetstorm":false,"jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":true,"jetpack_social_options":{"image_generator_settings":{"template":"highway","enabled":false}}},"categories":[2],"tags":[],"class_list":["post-47","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-maths"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"https:\/\/i0.wp.com\/img.examcoaching.in\/sum-of-numbers.jpg?fit=1200%2C630","jetpack_sharing_enabled":true,"jetpack_shortlink":"https:\/\/wp.me\/p7pDEj-L","jetpack-related-posts":[{"id":51,"url":"http:\/\/www.examcoaching.in\/blog\/51\/calculation-with-number-of-shake-hands","url_meta":{"origin":47,"position":0},"title":"Calculation with number of Shake hands","author":"Ranjith","date":"August 6, 2016","format":false,"excerpt":"PSC and other competitive exams always contains questions with shake hands. Lets see how can we solve the questions with shake hands Type 1: Find Shake hands if number of people is given Total Number of shake hands exchanged if n people shake hands each other = (n2-n)\/2 = (n(n-1))\/2\u2026","rel":"","context":"In "Maths"","block_context":{"text":"Maths","link":"http:\/\/www.examcoaching.in\/blog\/category\/maths"},"img":{"alt_text":"Calculations with number of shake hands","src":"https:\/\/i0.wp.com\/img.examcoaching.in\/number-of-shake-hands.jpg?fit=1200%2C630&resize=350%2C200","width":350,"height":200},"classes":[]},{"id":8,"url":"http:\/\/www.examcoaching.in\/blog\/8\/numbers","url_meta":{"origin":47,"position":1},"title":"Numbers","author":"Ranjith","date":"April 20, 2016","format":false,"excerpt":"A number is a mathematical object used to count, measure, and label. A notational symbol that represents a number is called a numeral. 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Indians widely describe Gandhi as the father of the nation. Gandhi\u2026","rel":"","context":"In "History"","block_context":{"text":"History","link":"http:\/\/www.examcoaching.in\/blog\/category\/history"},"img":{"alt_text":"People Known as Gandhi","src":"https:\/\/i0.wp.com\/img.examcoaching.in\/people-known-as-gandhi.jpg?fit=1000%2C625&resize=350%2C200","width":350,"height":200},"classes":[]}],"jetpack_likes_enabled":true,"_links":{"self":[{"href":"http:\/\/www.examcoaching.in\/blog\/wp-json\/wp\/v2\/posts\/47","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/www.examcoaching.in\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/www.examcoaching.in\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/www.examcoaching.in\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/www.examcoaching.in\/blog\/wp-json\/wp\/v2\/comments?post=47"}],"version-history":[{"count":3,"href":"http:\/\/www.examcoaching.in\/blog\/wp-json\/wp\/v2\/posts\/47\/revisions"}],"predecessor-version":[{"id":50,"href":"http:\/\/www.examcoaching.in\/blog\/wp-json\/wp\/v2\/posts\/47\/revisions\/50"}],"wp:featuredmedia":[{"embeddable":true,"href":"http:\/\/www.examcoaching.in\/blog\/wp-json\/wp\/v2\/media\/54"}],"wp:attachment":[{"href":"http:\/\/www.examcoaching.in\/blog\/wp-json\/wp\/v2\/media?parent=47"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/www.examcoaching.in\/blog\/wp-json\/wp\/v2\/categories?post=47"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/www.examcoaching.in\/blog\/wp-json\/wp\/v2\/tags?post=47"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}