Hello from MrBillDoesMath!
Answer:
First term = S(1) = 1
Common difference = S(n+1) - S(n) = 1 -6n
t(n) value: can't answer this as I don't know what t(n) refers to,
Discussion:
Let S(n) = 4n - 3n^2
First term:
S(1) = 4(1) - 3(1)^2 = 4 - 3 = 1
Common difference:
S(n+1) - S(n) = ( 4(n+1) - 3 (n+1)^2) - (4n - 3n^2)
= (4n + 4 - 3n^2 -6n -3) - 4n + 3n^2
(now cancel common terms)
= -6n + 4 - 3 = -6n + 1
S(n+1) = S(n) -6n + 1
Thank you,
MrB