Question 719677
Let {{{d_n}}} be the common difference between numbers n and n+1.

First look at the common difference between each term:

5-2 = 3   <---d1
15-5 = 10 <----d2
45-15 = 30 <----d3
135 - 45 = 90 <---d4
405 - 135 = 270 <----d5
1215- 405 = 810 <----d6

Notice that {{{d_1 * d_n}}} gives {{{d_(n+1)}}}.

So to find d7, we need to take 3 * 810 = 2430 which is the difference between 810 and the next number. So 2430 + 810 = 3240.