SOLUTION: the next number or item in the sequence:2- 5 15 45 135 405 1215

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Question 719677: the next number or item in the sequence:2- 5 15 45 135 405 1215
Answer by swincher4391(1107) About Me  (Show Source):
You can put this solution on YOUR website!
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+%2A+d_n gives d_%28n%2B1%29.
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.