Question

Whats the pattern for 1 4 9 16 25

Answer 1

This is a quadratic series and there a formula that u  can use to describe it:
$a+d(n-1) + \frac{c(n-1)(n-2)}{2}$
where a is the first term,d is the first  difference and c is the common difference
to get d subtract 1 from 4 which = 3
to get c subtract 4 from 9 to get   5 and then 5-3= 2
c=2

pluging the values into the formula we get:
$1+3(n-1)+ \frac{2(n-1)(n-2)}{2}$

simplifying it we get:
$n^{2}$
and this formula describes ur sequence 

n is the position of a value in a progression for instance in  your sequence:
4 is the second term its position can be expressed as n=2
9 is the third term its position can be expressed as n=3

so 1^2=1,
2^2=4,
3^2=9,
4^2=16
the sequence goes on to infinity

Answer 2

You add the numbers that were last in the list. Ex: 1 + 4 =5 + 9= 16 + 9 = 25. it's Fibonacci I believe