MATHEMATICS · Multi-part · A Level · Mathematics · Sequences and series · Sequences and series
Problem
Let
Sn=k=0∑n−1(7k+4).
Answer the questions below.
(i) Simplify Sn to an expression that is a polynomial in n. Do not leave the answer in summation form.
(ii) Hence find the numerical value of S20. Express your answer as an integer.
(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).