The formula nth

Question

Find the formula for 9,16,25 ,...

Thank you

Answer 1

The first tern in a series is a₁. That is, n=1.

The first term here is 9, which is (1+2)². Each term is (n+2)².
The formula for the series is:
a_n = (n+2)²      or       a_n = a²  + 4n + 4      [note: use F-O-I-L]

So,
a₁ = (1+2)² = 3² = 9
a₂ = (2+2)² = 4² = 16

etc.

Answer 2

If you count from 1 up ....

 

N.   N²

1 .   1

2 .   4

3.    9

4.    16

5 .   25

6.    36

 

This list is obvious.  BUT, in your problem, N started with 3 instead of 1.  So to make the series work, you need to add 2 before you square the number.

 

N.  (N+2)²

1 .   9

2.    16

3.    25 .       Etc.

 

If you multiply out (N+2)², you get N²+4N+4.

Answer 3

3^2 = 9

 

4^2 = 16

 

5^2 = 25

 

The next term in the sequence is 6^2 = 36

 

then 7^2 = 49

 

In general, the formula for the sequence is N^2 = N*N