Let the linear sequence (Arithmetic Progression, AP) have a first term a and a common difference d. The n^th term of an AP is given by A_n = a + (n−1)d.

Here's a step-by-step solution to the problem.

Let the linear sequence (Arithmetic Progression, AP) have a first term $a$ and a common difference $d$. The $n^{th}$ term of an AP is given by $A_n = a + (n-1)d$.

The $5^{th}$, $9^{th}$, and $16^{th}$ terms of the AP are:
$A_5 = a + (5-1)d = a + 4d$
$A_9 = a + (9-1)d = a + 8d$
$A_{16} = a + (16-1)d = a + 15d$

These three terms