Math Help: Sequences and series?

Question

Given the expression Sn= n^2 + 2n
a) values for S1 and S2
b) an exprssion in simplified form for S(n-1) in terms of n
c) an expression in simplified form for the nth term tn in terms of n.

Answer 1

a) Sn= n^2 + 2n
S1=1^2 + 2(1)
=1+2
=3#

S2=2^2 + 2(2)
=4+4
=8#

b) S(n-1)=(n-1)^2 + 2(n-1)
=n^2-2n+1+2n-2
=n^2-1
=(n+1)(n-1)#

c)Tn=Sn-S(n-1)
=(n^2 + 2n)-(n^2-1)
= n^2 + 2n-n^2+1
=2n+1#

Answer 2

a)
S(1) = 3
S(2) = 8
B)
S(n - 1) = (n - 1)(n + 1) = n^2 - 1
C)
S(n) = n(n + 2)