If 2k+1,6,3k+1 are in a. p then find the value of k

Solution :

We know that ,

If a , b, c are in A.P then

b - a = c - b

Here ,

a = 2k+1 , b = 6 , c = 3k+1 are in A.P.

b - a = c - b

=> 6 - ( 2k + 1 ) = ( 3k + 1 ) - 6

=> 6 - 2k - 1 = 3k + 1 - 6

=> -2k + 5 = 3k - 5

=> -2k - 3k = -5 - 5

=> -5k = -10

⇒ k = ( -10 )/( -5 )

⇒ K = 2

Therefore ,

k = 2

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