The value of k for which the numbers x, 2x+k, 3x+6 are in A. P. Is?

1.	The value of k for which the numbers x, 2x+k, 3x+6 are in A. P. Is?
Answer» It is given that ,x\xa0,2x+k\xa0and\xa03x+6\xa0are\xa0three\xa0consecutive\xa0terms\xa0.we\xa0know\xa0that\xa0,Difference\xa0of\xa0any\xa0two\xa0consecutive\xa0terms\xa0is\xa0equal\xa0in\xa0A.P\xa0Now,(2x+k)-x\xa0=\xa0(3x+6)-(2x+k)=>\xa02x+k-x\xa0=\xa03x+6-2x-k=>\xa0x+k\xa0=\xa0x+6-k=>\xa0k+k\xa0=\xa0x+6-x=>\xa02k\xa0=\xa06=>k\xa0=\xa06/2=>\xa0k\xa0=\xa03Therefore,If\xa0k\xa0=\xa03\xa0then the given three consecutive terms x,2x+k and 3x+6 are in\xa0A.P

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