Let
Sn=k=0∑n−1(7k+4).
Answer the questions below.
a. (i) Simplify Sn to an expression that is a polynomial in n. Do not leave the answer in summation form.
b. (ii) Hence find the numerical value of S20. Express your answer as an integer.
c. (iii) For n=20, re-calculate the sum by pairing the first and last term, the second and second-last term, and so on. Show that the result agrees with part (ii).