TITLE: How to solve this sequence $165,195,255,285,345,x$
QUESTION [13 upvotes]: This is a question appeared in a competitive exam. The question is:   

Find the unknown term in $165,195,255,285,345,x$   
1)375 $\ \ \ \ \ \ \ \ $               2)420
  3)435 $\ \ \ \ \ \  \ $            4)390   

My Research Effort 
$$a_n =
\begin{cases}
a_{n-1}+30,  & \text{if $n$ is even} \\
a_{n-1}+60, & \text{if $n$ is odd}  \\
\end{cases}$$
where $n>1$
$a_1=165$. In this way the answer should be $a_6=375$. BUT this is not the correct answer. Any hints will be appreciated.
Thanks in advance.

REPLY [4 votes]: 375 is the answer. Though I don't treat such questions as mathematical question. But they do appear in competitive exams and are base on kind of pattern recognition.
Look at the sequence:
165,(+30)=195 ,(+60)=225,(+30)=285,(+60)=345,(+30)=375