Determine whether the sequence is arithmetic, geometric, both, or neither.
1, 4, 9, 16, 25, . .
Neither. What you have here is a series for the squares for the Natural numbers.
1^2 , 2^2 , 3^2, 4^2, .......... n^2
To be an a.p. a series must have a common difference. ie if you subtract a term from its successor,you should always get the same answer. Clearly 2^2 - 1^2 is not the same as 3^2 - 2^2.
To be a g.p. a series must have a common ratio,ie if you divide a term by its predecessor you always get the same answer. 4^2 / 3^2 is not the same as 3^2 - 2^2.
There is,by the way,a formula for the sum of the squares of the Natural numbers,but I'll let you look at that for yourself.
