The four positive numbers are consecutive terms of a certain sequence

MATHEMATICS · Subjective · A Level · Mathematics · Sequences and series · Sequences and series

Problem

The four positive numbers

9,\,p,\,q,\,243

are consecutive terms of a certain sequence. (i) Given that

\log_{3} 9,\,\log_{3} p,\,\log_{3} q,\,\log_{3} 243

form an arithmetic progression, find the values of

p

and

q

. (ii) Using the values of

p

and

q

, obtain the general term

a_n

of the sequence. (iii) Evaluate the sum of the first six terms of the sequence.