math

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sandra wrote the sequence below
2,5,10,17,...
which equation represents the rule for finding the nth term of this equation

• math -

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?

• math -

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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