OK, here is the answer, but I'm not sure I can even explain it!! The next 3 numbers are 183, 285, and 421. Here's how it works:
First, I figured out what number added to the previous number would give the next number:
5+3=8
8+7=15
15+16=31
31+30=61
61+49=110
Next, try to find a pattern that will tell you what to add to 110 to get the next number. Hint: look at the numbers that are added to the original numbers in your sequence: 3, 7, 16, 30, 49. Try to figure out how to find the next number in THAT sequence, and you will have the next number in your original sequence. Ok, I'll post the rest because I am so afraid of forgetting what I did, but try to get it yourself first.
SPOILER AHEAD
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OK, now if you look closely at the numbers we came up with to add to the original numbers (3, 7, 16, 30, 49), do you see another pattern when you do the same thing we did originally??
3+4=7
7+9=16
16+14=30
30+19=49
49+????
what are you adding each time to the number? FIVE!!
So, next you have 49+24 (because 19+5=24) =73
Add 73 to 110 to get the next number in your sequence: 183!
OK, you'll have to do the rest on your own, and I hope I didn't do a bad thing by posting the answer, but it is late and I might not remember what I did tomorrow!!!
Good luck!!!!