Is -150 a term of AP 17,12,7,2
Posted by Alok Raj 3 years, 1 month ago
The given term of arithmatic progression is17, 12, 7, 2, ...... Here, a = 17, d = 12 - 17 = - 5 where a is first term and d is common difference Suppose an = -150 a + (n - 1)d = -150 {tex}\Rightarrow{/tex} 17 + (n - 1)(-5) = -150 {tex}\Rightarrow{/tex} (n - 1)(-5) = -150 - 17 {tex}\Rightarrow{/tex} (n - 1)(-5) = -167 {tex}\Rightarrow{/tex} n - 1 = {tex}\frac { 167 } { 5 }{/tex} {tex}\Rightarrow{/tex} n = {tex}\frac { 167 } { 5 }{/tex} + 1 {tex}\Rightarrow{/tex} n = {tex}\frac { 167 + 5 } { 5 } = \frac { 172 } { 5 } = 34 \frac { 2 } { 5 }{/tex}where n is not a whole number. {tex}\therefore{/tex} -150 is not a term of the A.P. -150 is not a term of the given A.P.Given, First term \(= a = 17\) Common difference \(= d = -5\)As we know, For the \(n\)th term, \({T_n} = a + (n - 1)d\) \( - 150 = 17 + (n - 1)( - 5)\) \((n - 1) = \frac{{ - 167}}{{ - 5}} = 33.4\) \(n = 33.4 + 1 = 34.4\) Hence \(n\) = 34.4 which is in decimal so -150 is not a term of A.P. Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts Dedicated counsellor for each student Detailed Performance Evaluation view all coursesPage 2Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts Dedicated counsellor for each student Detailed Performance Evaluation  |
Check whether - 150 is a term of the ap 17 12 7 2
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