Squaddy

I am sorry for any problems you might have had reading, but  "{nl}" is not supposed to be there so just ignore them.

Also I seem to be unable to edit my answer

Assuming the ratio doesn't change, you can divide any of the numbers with the previous one to find the ratio.

For example: {nl} \(150/100=1.5\) {nl} {nl} We can test this by applying this value to the other numbers in the sequence:

\(150*1.5=225\) {nl} \(225*1.5=337.5\) {nl} \(337.5*1.5=506.25\)

We have confirmed that the ratio from one number to the next is 1.5 {nl} To find the percentage we multiply a ratio with 100:

\(1.5*100=150\)

The answer is 150 %. 

The tangent is the ratio between the opposite side and the adjacent side of a right triangle.

$$\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{tan}}{\left({\mathtt{x}}\right)} = {\frac{{\mathtt{opposite}}}{{\mathtt{adjacent}}}}$$

$$\left({\mathtt{2}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{5}}}{{\mathtt{8}}}}\right){\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{9}}}{{\mathtt{16}}}}{\mathtt{\,\small\textbf+\,}}\left({\mathtt{3}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{1}}}{{\mathtt{4}}}}\right)$$

$${\frac{{\mathtt{5}}}{{\mathtt{8}}}} = {\mathtt{0.625}}$$        $${\frac{{\mathtt{9}}}{{\mathtt{16}}}} = {\mathtt{0.562\: \!5}}$$      $${\frac{{\mathtt{1}}}{{\mathtt{4}}}} = {\mathtt{0.25}}$$

Start inside the brackets:

$$\left({\mathtt{2}}{\mathtt{\,\small\textbf+\,}}{\mathtt{0.625}}\right){\mathtt{\,\small\textbf+\,}}{\mathtt{0.562\: \!5}}{\mathtt{\,\small\textbf+\,}}\left({\mathtt{3}}{\mathtt{\,\small\textbf+\,}}{\mathtt{0.25}}\right)$$

$$\left({\mathtt{2.625}}\right){\mathtt{\,\small\textbf+\,}}{\mathtt{0.562\: \!5}}{\mathtt{\,\small\textbf+\,}}\left({\mathtt{3.25}}\right)$$

Then you just add the numbers:

$${\mathtt{2.625}}{\mathtt{\,\small\textbf+\,}}{\mathtt{0.562\: \!5}}{\mathtt{\,\small\textbf+\,}}{\mathtt{3.25}} = {\mathtt{6.437\: \!5}}$$

In order to find the decimals you simply divide the two numbers:

$${\frac{{\mathtt{8}}}{{\mathtt{20}}}} = {\mathtt{0.4}}$$

The decimal is 0.4

If you want to find the precentage you take the decimal and multiply it by 100:

$${\mathtt{0.4}}{\mathtt{\,\times\,}}{\mathtt{100}} = {\mathtt{40}}$$

The percentage is 40%