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I the lines a x+12 y+1=0,\ b x+13 y+1=0 ...

I the lines `a x+12 y+1=0,\ b x+13 y+1=0` and `c x+14 y+1=0` are concurrent, then `a , b , c` are in a. H.P. b. G.P. c. A.P. d. none of these

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Since the given lines are concurrent ∴`[[a,12,1],[b,13,1],[c,14,1]]=0`
`=>[[a,12,1],[b-a,1,0],[c-b,1,0]]=0`
[Applying `R3→ R3−R2, R2→R2−R1]`
`=>b−a−c+b=0`
or` 2b=a+c=>a,b,c` are in`A.P`.
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