Question

write set bulder form of {1,5,10,17,26}

Answer 1

You have a sequence 

2,5,10,17,26 
first find the differences 
3,5,7.9 
now these also have differences ... called second differences 
2,2,2 

Matching Second differences implies Squares 

So write the squares 
1², 2²,3² etc 
1,4,9,16,25 ....and look carefully at them 
and now match them to your numbers 
1,4,9,16,25 
2,5,10,17,26......see the change 

Your sequence is the squares + 1 

You formula is 

n² +1 .................this generates your SET but you must state your Limits 

n² +1 where Integer n>0