For what value of k k+9 , 2k-1 and 2k+7 are consecutive terms of an AP

1.	For what value of k k+9 , 2k-1 and 2k+7 are consecutive terms of an AP??
Answer» {tex}mx - ny = m^2 + n^2{/tex} ...(i){tex}x + y = 2m{/tex} ...(ii)Multiplying equation (ii) by m and subtracting from (i), we get{tex}y = \\frac { n ^ { 2 } - m ^ { 2 } } { - ( m + n ) }{/tex}\xa0= -\xa0{tex}\\frac { ( n - m ) ( n + m ) } { m + n }{/tex}y = m - nPutting value of y in (i), we get{tex}mx - n(m - n) = m^2 + n^2{/tex}{tex}mx - nm + n^2 = m^2 + n^2\xa0{/tex}{tex}mx = m^2 + nm ={/tex}\xa0{tex}\\frac{m(m + n)}{m}{/tex}{tex}x = m + n{/tex}

Discussion