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**Hint:**The full form of AP is Arithmetic progression. It is a mathematical sequence in which the difference between two consecutive terms is always a constant.

In this progression, for a given series, the terms used are the first term, the common difference between the two terms and nth term. Suppose, ${a_1},{a_2},{a_3},{a_4},......{a_n}$ is an AP, then the common difference‘d’ can be obtained as:

$d = {a_2} - {a_1} = {a_3} - {a_2} = ...... = {a_n} - {a_{n - 1}}$

Where‘d’ is a common difference, it can be positive, negative or zero.

**Complete step by step answer:**

Given that $5,k,11$ are in AP,

AP stands for Arithmetic progression. If these three terms are in Arithmetic progression then the difference between any two consecutive terms should be the same.

First term$ = 5$

Second term$ = k$

Third term$ = 11$

$\therefore $ Second term$ - $ First term$ = $ Third term$ - $ Second term

$ \Rightarrow k - 5 = 11 - k$

$ \Rightarrow k + k = 11 + 5$

$ \Rightarrow 2k = 16$

$ \Rightarrow k = \dfrac{{16}}{2}$

$ \Rightarrow k = 8$

Hence the value of k is $8$.

**Note:**

In mathematics, there are three different types of progressions. They are:

Arithmetic Progression (AP)

Geometric Progression (GP)

Harmonic Progression (HP)

Arithmetic Progression (AP) - A sequence of numbers is called an arithmetic progression if the difference between any two consecutive terms is always the same.

Geometric Progression (GP) – A sequence of numbers is called an arithmetic progression if the difference between any two consecutive terms is always the same

Harmonic Progression (HP) – A sequence of numbers is called a harmonic progression if the reciprocal of the terms are in Arithmetic Progression.

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