Pattern

It is a Fibonacci-like sequence . The general formula is: $a_n = a_{n-1} + a_{n-2}$ as follows:

$\begin{aligned} a_{n-2} + a_{n-1} & = a_n \\ 205 + 210 & = 415 \\ 210 + 415 & = 625 \\ 415 + 625 & = 1040 \\ 625 +1040 & = 1665 \\ 1040 + 1665 & = 2705 \\ 1665 + 2705 & = 4370 \\ 2705 + 4370 & = 7075 \\ 4370 + 7075 & = 11445 \\ 7075 + 11445 & = \boxed{18520} \end{aligned}$

Relevant wiki: Fibonacci Sequence

$205 + 210 = 415$

$415 + 210 = 625$

$625 + 415 = 1040$

$1040 + 625 = 1665$

$1665 + 1040 = 2705$

$2705 + 1665 = 4370$

$4370 + 2705 = 7075$

$7075 + 4370= 11445$

$11445 + 7075= 18520$