Consider an arithmetic progression whose first term is 7 and common difference is 3. The progression contains (2n+1) terms.
a. (i) Write the last term of the progression in terms of n.
b. (ii) Derive an expression for the sum S of all (2n+1) terms in terms of n.
c. (iii) Simplify your expression for S.
d. (iv) Using your result, find the value of S when n=12.