Mathematics

Problem

Consider the process of inserting three numbers between two unequal real numbers

p

and

q

so that the five numbers in order form an arithmetic progression. a. (i) State the general term

a_n

of an arithmetic progression whose first term is

a

and common difference is

d

. b. (ii) Show that, for the progression described above, the common difference equals

\dfrac{q-p}{4}

. c. (iii) Using the result of part (ii), determine the three numbers that must be inserted between

2

and

14

to obtain an arithmetic progression.