Question

For what value of k will k + 9,2k -1 and 2k + 7 are the consecutive terms of an A.P.?

Answer 1

Answer:

The value of k is 18

Step-by-step explanation:

Given that,

k+9, 2k-1, 2k+7 are consecutive integers of an AP

So their common difference are equal

2k-1-(k+9) = 2k+7-(2k-1)

2k-1-k-9 = 2k+7-2k+1

k-10 = 8

k=18

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Answer 2

Answer: 18

Step-by-step explanation:

Let the first term of an A.P. be a and the common difference be d.

Then three consecutive terms would look like: a, a + d, a + 2d

In an A.P. mean of the first and third term is equal to the second term

Proof:

Mean of 1st and 3rd term = [a + (a+2d)]/2

                                          = [ 2a + 2d ]/2

                                          = a + d

Therefore,

                           2k - 1      =     [(k + 9) + (2k + 7)]/2

             =>          4k - 2     =       3k + 16

             =>            k           =        18