Question

Please explain the formula on how to solve question like these ...

Study the pattern and predict the nth term

a) 2,5,10,17 ...

b) 0,1,4,9 ...

I got the answers just I don't understand the formula

Answer 1

There's not really a "Formula," but you can give an explanation for how you try to find the pattern.

Answer 2

Have you tried making an input-ouput chart? (:

Answer 3

It can help you find what the "formula" is. It's different for each sequence/pattern

Answer 4

well what i got wel "learned but dont get" is

term 1 term 2
2 5
n=1 n=2
1+1 2+3
1+1^2
1+n^2

so what i am trying to figure out is do you just try and try ???

Answer 5

Well, yes. But you can try in smart ways. Like, I know some common sequences, and I check those first. Here was my thought process for this.
Is it arithmetic? No. There is not a common difference each time.
Is it geometric? No. There is not a common ratio each time.
Well, what are the differences? From term1 to term2 is 3. From term2 to term3 is 5. From term3 to term4 is 7. Oh, the difference increases by 2 each time.

Answer 6

I see and I did that thought process too but when i tried to plug it in it didn't work

the answer is 1+n^2

so we have to square the the term and add one

how on earth do you get that in your head ? or am I just being stupid and need to think a ton harder on these questions since it is all in the brain ?

Answer 7

^^ Yeah (: It's not really a formula you see? You just need to state that the difference increases by 2 each time.

Answer 8

mmm okay thanks so much for all your help :) lets pray that these quistions dont count too much on the final :[