Mathematics

Problem

The sum of the first

n

terms of a sequence is given by

S_n = 4n^2 + 3n

. a. (a) Obtain an expression for the

n

th term

a_n

of the sequence. b. (b) Show that the sequence whose terms are

a_1, a_2, a_3, \ldots

forms an arithmetic progression. c. (c) Find the first term and the common difference of this progression. d. (d) Calculate the 20th term.