The first three terms of a sequence are 3p−5, 2p+1 and p+7.
a. (i) Show that these three terms are in arithmetic progression only for a particular value of p and find that value.
b. (ii) For the value of p obtained in part (i), write the next two terms of the progression.
c. (iii) For the same value of p, determine the term number whose value will be 52.