Question

Q 3. If 3x + k, 2x + 9 and x + 13 are three consecutive terms of
an AP. Then find k
​

Answer 1

Answer:

The value of k is 5.

Step-by-step explanation:

Given,

     $3x + k, 2x + 9 \hspace{2mm}and \hspace{2mm} x + 13$ are the three terms  in A.P.

For terms in A.P, There is constant difference between two consecutive terms.

So,

        Difference between first and second term= Difference between 2nd and 3rd terms.

            $(2x+9)-(3x+k)=(x+13)-(2x+9)\\ \\ 2x+9-3x-k=x+13-2x-9\\ \\ 2x-3x-k+9=x-2x+13-9\\ \\ -x-k+9=-x+4\\ \\ -k+9=4\\ \\ k=9-4=5$

so the value of k =5.