Brain Teasers
2, 5, 7, 10, 13, 15, 18, 20...
What are the next five terms in this sequence?
2, 5, 7, 10, 13, 15, 18, 20, 23, 26, 28, 31, 34, 36, 39, 41, 44, 47, 49, 52...
2, 5, 7, 10, 13, 15, 18, 20, 23, 26, 28, 31, 34, 36, 39, 41, 44, 47, 49, 52...
Hint
Each term is 2 or 3 greater than its preceding term, but this is not all.Answer
The pattern is: the nth term in this sequence is n greater than the nth natural number that is NOT contained in this sequence.2=1+1, 5=3+2, 7=4+3, 10=6+4, 13=8+5, 15=9+6, 18=11+7, 20=12+8, 23=14+9, 26=16+10, 28=17+11, 31=19+12, 34=21+13, 36=22+14, 39=24+15, 41=25+16, 44=27+17, 47=29+18, 49=30+19, 52=32+20.
Therefore, the next five terms are: 54=33+21, 57=35+22, 60=37+23, 62=38+24, 65=40+25.
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Comments
Didn't get it... a little too obscure for me.
It is only difficult, not obscure, because I have given the first 20 terms.
If I had given only the first 10 terms, it would have been obscure.
If I had given only the first 10 terms, it would have been obscure.
How could you express this pattern in a formula?
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