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What are the next 5 terms of this sequence and what is the formula, or the generating function?
10, 35, 46, 80, 82, 125, 118, 170, 154, 215, 190, 260, 226, 305, 262, 350...........etc.
Thanks a lot for any help. 

 Oct 7, 2019
 #1
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Notice that the odd-numbered terms, 1, 3, 5, 7........etc have a difference of 36, and the even-numbered terms, 2, 4, 6.....etc,  have a difference of 45!!.

 

So, the next 5 terms  are: 262+36=298, 350+45 =395, 298+36 =334, 395+45=440, 334+36=370.

So, the next 5 term are:298, 395, 334, 440, 370.......etc.

 Oct 7, 2019
 #2
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I noticed that this sequence alternates between the sum of first 4 counting numbers and the sum of the next 5 counting numbers: [1+2+3+4=10], [5+6+7+8+9=35], [10+11+12+13=46], [14+15+16+17+18=80]....etc.

 Oct 8, 2019
edited by Guest  Oct 8, 2019

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