Determine k so that k+2,k-6,3k-2 are the three consecutive terms of an

1.	Determine k so that k+2,k-6,3k-2 are the three consecutive terms of an A.P
Answer» Since {tex}(3k-2), (4k-6)\\ and \\ (k+2){/tex} are in AP, we have\xa0{tex}(4k-6)-(3k-2)=(k+2)-(4k-6){/tex}{tex}\\Rightarrow{/tex}\xa0{tex}4k - 6 - 3k + 2 = k + 2 - 4k + 6{/tex}{tex}\\Rightarrow{/tex}\xa0{tex}k - 4 = -3k + 8{/tex}{tex}\\Rightarrow{/tex}\xa04k = 12{tex}\\Rightarrow{/tex}\xa0k = 3.

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