sandra wrote the sequence below

2 answers

1. 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?

   Answer ID
   524521

   Created
   April 3, 2011 3:01am UTC

   Rating
   0

   URL
   https://questions.llc/answers/524521

2. 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.

   Answer ID
   524804

   Created
   April 3, 2011 9:08pm UTC

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   0

   URL
   https://questions.llc/answers/524804