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For what value of $k$ are $2k-7$, $k+5$ and $3k+2$ consecutive terms of an Arithmetic Progression?

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    Well, $3k + 2 = (k + 5) + d, 3k + 2 = (2k -7) + 2d$, etc. Can you take it from here?2012-10-30
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    You’ve been working with arithmetic progressions for a while now; do you have any ideas on how to proceed?2012-10-30
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    Yes, It's my one of the favourite topic in Mathematics. And now I know that how can we proceed but, I am feeling difficulty in finding the relation between the given variable terms to get an AP from it.2012-10-30
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    Another useful thing to remember is that the sum of three consecutive terms of an arithmetic progression is equal to three times the middle term. If the terms can be taken out of order (i.e. they are three consecutive terms of a progression, but not in order) there is a second value of $k$ to be found.2012-10-30

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Hint: The numbers $a,b,c$ are consecutive terms of an AP if and only if $c-b=b-a$.