What is the next two terms of the series 1, 5, 17, 43, 89?

Answer 1

I think the answer is 161 and 265.
But I'm being too stupid to work out what the formula is in terms of n so it may not be right.

The way I did it was to find the difference between all the numbers which was 4,12,26 and 46. (eg 5-1=4, 17-5=12 etc) The difference between all of those is then 8 14 and 20 (eg 12-4). The diffence between all of these is 6. (14-8=6,20-14=6)

If the difference is constantly six on this line, this means that the difference between the numbers on the line above is also six, so 20+6=26, +6=32.

Then, on the line above, 46+26=72, 72+32=104.

Now you're back on the line you're using. After 89, we worked out the next difference is 72, therefore 89+72=161, and 161+104=265.

I have no idea if this made sense to you or if the solution is even right (it would really help if I could work out what the actual formula is but it isn't coming to me at the moment ><) but I hope this helps all the same..

Edit: Just checked back to see the post after mine. Yay my numbers were right lol!

Answer 2

the numbers fit the formula a[n] = n³ - 2n² + 3n - 1, so
a[6] = 161 and a[7] = 265