Question

what is the nth term of 1,4,9,16,25

Answer 1

the reason that you give (d changes). The formula is ONLY for arithmetic sequences where d remains constant.

The sequence 4, 9, 16, 25, ... is not arithmetic, but 4, 9, 16, 25,... are perfect squares.

a1 = 4 = 22

a2 = 9 = 32

a3 = 16 = 42, etc

So, we could define the sequence as an = (n+1)2, for n = 1,2,3,...