S(n+1)=S(n)+4(n+1)-3

Solution for S(n+1)=S(n)+4(n+1)-3 equation:

Simplifying
S(n + 1) = S(n) + 4(n + 1) + -3

Reorder the terms:
S(1 + n) = S(n) + 4(n + 1) + -3
(1 * S + n * S) = S(n) + 4(n + 1) + -3
(1S + nS) = S(n) + 4(n + 1) + -3

Multiply S * n
1S + nS = nS + 4(n + 1) + -3

Reorder the terms:
1S + nS = nS + 4(1 + n) + -3
1S + nS = nS + (1 * 4 + n * 4) + -3
1S + nS = nS + (4 + 4n) + -3

Reorder the terms:
1S + nS = 4 + -3 + 4n + nS

Combine like terms: 4 + -3 = 1
1S + nS = 1 + 4n + nS

Add '-1nS' to each side of the equation.
1S + nS + -1nS = 1 + 4n + nS + -1nS

Combine like terms: nS + -1nS = 0
1S + 0 = 1 + 4n + nS + -1nS
1S = 1 + 4n + nS + -1nS

Combine like terms: nS + -1nS = 0
1S = 1 + 4n + 0
1S = 1 + 4n

Solving
1S = 1 + 4n

Solving for variable 'S'.

Move all terms containing S to the left, all other terms to the right.

Divide each side by '1'.
S = 1 + 4n

Simplifying
S = 1 + 4n