{"id":1516,"date":"2022-11-21T16:00:33","date_gmt":"2022-11-21T10:30:33","guid":{"rendered":"https:\/\/www.aplustopper.com\/?p=1516"},"modified":"2022-11-22T16:51:17","modified_gmt":"2022-11-22T11:21:17","slug":"arithmetic-mean","status":"publish","type":"post","link":"https:\/\/www.aplustopper.com\/arithmetic-mean\/","title":{"rendered":"What Is Arithmetic Mean"},"content":{"rendered":"
If three or more than three terms are in A.P., then the numbers lying between first and last term are known as Arithmetic Means between them.i.e. Example 1:<\/strong> \u00a0 \u00a0If 4 AM\u2019s are inserted between 1\/2 and 3 then find 3rd AM. Example 2: \u00a0 \u00a0<\/strong>n AM\u2019s are inserted between 2 and 38. If third AM is 14 then find n. What Is Arithmetic Mean If three or more than three terms are in A.P., then the numbers lying between first and last term are known as Arithmetic Means between them.i.e. The A.M. between the two given quantities a and b is A so that a, A, b are in A.P. i.e. A \u2013 a = […]<\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_genesis_hide_title":false,"_genesis_hide_breadcrumbs":false,"_genesis_hide_singular_image":false,"_genesis_hide_footer_widgets":false,"_genesis_custom_body_class":"","_genesis_custom_post_class":"","_genesis_layout":"","footnotes":""},"categories":[5],"tags":[393,395,394,340],"yoast_head":"\n
\nThe A.M. between the two given quantities a and b is
\nA so that a, A, b are in A.P.
\ni.e. A \u2013 a = b \u2013 A
\n\\( \\Rightarrow A=\\frac{a+b}{2} \\)
\nNote:<\/strong> A.M. of any n positive numbers a1<\/sub>, a2<\/sub> ……an<\/sub> is
\n\\( A=\\frac{{{a}_{1}}+{{a}_{2}}+{{a}_{3}}+…..{{a}_{n}}}{n} \\)
\nn AM\u2019s between two given numbers<\/strong>
\nIf in between two numbers \u2018a\u2019 and \u2018b\u2019 we have to insert n AM A1<\/sub>, A2<\/sub>,\u00a0…..An then a, A1<\/sub>, A2<\/sub>, A3<\/sub>….An<\/sub>, b will be in A.P. The series consist of (n + 2) terms and the last term is b and first term is a.
\na + (n + 2 \u2013 1) d = b
\n\\( d=\\frac{b-a}{n+1} \\)
\nA1<\/sub> = a + d, A2<\/sub> = a + 2d, …… \u00a0An<\/sub> = a + nd \u00a0 \u00a0 \u00a0 or
\nAn<\/sub> = b \u2013 d
\nNote:<\/strong>
\n(i)<\/strong> Sum of n AM\u2019s inserted between a and b is equal to n times the single AM between a and b i.e.
\n\\( \\sum\\limits_{r\\,=\\,1}^{n}{{{A}_{r}}}=nA\\text{ Where }A=\\frac{a+b}{2} \\)
\n(ii)<\/strong> between two numbers
\n\\( =\\frac{sum\\,of\\,m\\,AM’s}{sum\\,of\\,n\\,AM’s}=\\frac{m}{n} \\)<\/p>\nArithmetic Mean Examples<\/strong><\/h2>\n
\nSolution. \u00a0<\/strong>\u00a0Here
\n\\( d=\\frac{3-\\frac{1}{2}}{4+1}=\\frac{1}{2} \\)
\n\u2234 \u00a0A3<\/sub> = a + 3d
\n\\( \\Rightarrow \\frac{1}{2}+3\\times \\frac{1}{2}=2 \\)<\/p>\n
\nSolution. \u00a0\u00a0<\/strong> Here 2 + 3d = 14 \u21d2 d = 4
\n\\( \\therefore 4=\\frac{38-2}{n+1} \\)
\n\u21d2 4n + 4 = 36
\n\u21d2 n = 8<\/p>\n","protected":false},"excerpt":{"rendered":"