what do ypu mean by A.P

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what do ypu mean by A.P

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Given three terms are in A.P so,2(2k-1)=k+2k+1;4k-2=3k+1;4k-3k=1+2;k=3
Therefore k=3

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If three terms are in AP, then sum of the first and third are twice the middle.

k + 2 k +1 = 2 (2k -1)

k = 3

so 3, 5, 7 are in AP

k + 2 k +1 = 2 (2k -1)

k = 3

so 3, 5, 7 are in AP