Given the expression Sn = n^2 + 2n for the sume of the first n terms of a series, determine

a) An expression, in simplified form, for Sn-1 in tmers of n
b) an expression, in simplified form, for the nth terms, tn in terms of n

a) To find an expression for Sn-1 in terms of n, we substitute (n-1) for n in the original expression Sn = n^2 + 2n.

So, we have:
Sn-1 = (n-1)^2 + 2(n-1)

Expanding the squared term:
Sn-1 = (n^2 - 2n + 1) + 2(n-1)

Simplifying further:
Sn-1 = n^2 - 2n + 1 + 2n - 2

Combining like terms, we get:
Sn-1 = n^2 - 1

Therefore, the expression for Sn-1 in terms of n is n^2 - 1.

b) To find an expression for the nth term, tn, in terms of n, we can subtract Sn-1 from Sn.

So, tn = Sn - Sn-1

Substituting the expressions we found earlier:
tn = (n^2 + 2n) - (n^2 - 1)

Expanding and simplifying:
tn = n^2 + 2n - n^2 + 1

Combining like terms, we get:
tn = 2n + 1

Therefore, the expression for the nth term, tn, in terms of n is 2n + 1.