Posted by jayla on Saturday, April 2, 2011 at 10:44pm.
did you notice that each term is one larger than a perfect square, ....
2 = 1^2 + 1
5 = 2^2 + 1
10 = 3^2 + 1
17 = 4^2 + 1
.
.
so what do you think?
The numbers are increasing by 3 then 5 then 7 then 9. Next, notice that every number is actually one more than a square number.
So the general formula is:
a(n)=1+n^2
Let's check:
a(1)=1+1^2=1+1=2
a(2)=1+2^2=1+4=5
a(3)=1+3^2=1+9=10
a(4)=1+4^2=1+16=17
We see it's correct.
The next numbers in the sequence should be:
a(5)=1+5^2=1+25=26
a(6)=1+6^2=1+36=37 etc.
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