$\"\"$

\

The sequence is $\"\"$

\

Calculate the difference of the sequence.

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

The difference are not equal.

\

So the sequence is $\"\"$

\

Find the second difference.

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

The second difference are not equal.

\

So the sequence is $\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

The third difference are not equal.

\

So the sequence is $\"\"$

\

$\"\"$

\

$\"\"$

\

Hence the fourth difference are equal, the series is in fouth degree polynomial.

\

$\"\"$

\

The general form of $\"\"$ -terms of fouth degree polynomial: $\"\"$ .

\

Substitute $\"\"$ and $\"\"$ in the general form.

\

$\"\"$

\

Substitute $\"\"$ and $\"\"$ in the general form.

\

$\"\"$

\

Substitute $\"\"$ and $\"\"$ in the general form.

\

$\"\"$

\

Substitute $\"\"$ and $\"\"$ in the general form.

\

$\"\"$

\

Substitute $\"\"$ and $\"\"$ in the general form.

\

$\"\"$

\

Solve the equation $\"\"$ and equation $\"\"$ .

\

$\"\"$

\

Solve the equation $\"\"$ and equation $\"\"$

\

$\"\"$

\

$\"\"$

\

Solve the equation $\"\"$ and equation $\"\"$ .

\

$\"\"$

\

Solve the equation $\"\"$ and equation $\"\"$ .

\

$\"\"$

\

Solve the equation $\"\"$ and equation $\"\"$ .

\

$\"\"$

\

Solve the equation $\"\"$ and equation $\"\"$ .

\

$\"\"$

\

Solve the equation $\"\"$ and equation $\"\"$ .

\

$\"\"$

\

$\"\"$

\

Solve the equation $\"\"$ and equation $\"\"$ .

\

$\"\"$

\

Solve the equation $\"\"$ and equation $\"\"$ .

\

$\"\"$

\

Solve the equation $\"\"$ and equation $\"\"$ .

\

$\"\"$

\

$\"\"$ .

\

Substitute $\"\"$ in the equation $\"\"$ .

\

$\"\"$

\

$\"\"$

\

Substitute $\"\"$ and $\"\"$ in the equation $\"\"$ .

\

$\"\"$

\

Substitute $\"\"$ , $\"\"$ and $\"\"$ in the equation $\"\"$ .

\

$\"\"$

\

Substitute $\"\"$ , $\"\"$ , $\"\"$ and $\"\"$ in the equation $\"\"$ .

\

$\"\"$

\

Substitute $\"\"$ , $\"\"$ , $\"\"$ and $\"\"$ , $\"\"$ in the general form of quadratic equation.

\

$\"\"$

\

$\"\"$

\

The $\"\"$ -terms of quardatic equation form $\"\"$ .

\

$\"\"$

\

The $\"\"$ -terms of quardatic equation form $\"\"$ .