An input is given, and some mathematical operations are performed in each step to obtain the next step. Identify the operations and answer the questions

What is the output if the input is 7?

We see the following mathematical operations at each step:

Input = x

Step 1: Calculating the value of x(x + 1)

Step 2: Adding half of the above outcome to it, which is $$x\ (x+1)\ +\ \dfrac{x\ \left(x\ +\ 1\right)}{2}\ =\ \dfrac{3}{2}x\ \left(x\ +\ 1\right)$$

Step 3: Multiplying the outcome of the previous step with 5 and removing 10, which is $$\ \dfrac{15}{2}x\ \left(x\ +\ 1\right)-\ 10$$

Step 4: Multiplying the outcome of the previous step with $$\dfrac{2}{5}$$, which is $$\ 3x\ \left(x\ +\ 1\right)-\ 4$$

Step 5: Dividing the previous term by 2 and square the term which is $$\left(\dfrac{3x\ \left(x\ +\ 1\right)}{2}-\ 2\right)^{^2}$$

The input given is 7 and the output can be calculated as,

$$\ Output\ =\left(\dfrac{3\times\ 7\ \times\ 8}{2}-\ 2\right)^{^2}\ =\ 82^2\ =\ 6724\ $$

The correct answer is option A.