Answer the following questions relating to the possibility of forming a geometric…
MATHEMATICS · Subjective · CBSE · Mathematics · Sequences and Series · Sequences and Series
Problem
Answer the following questions relating to the possibility of forming a geometric progression that begins with 5 and ends with –40.
(i) Explain why no real number can be placed between 5 and –40 so that 5, the inserted number and –40 are consecutive terms of a geometric progression.
(ii) Decide, with clear reasoning, whether it is possible to place exactly two real numbers between 5 and –40 so that the resulting sequence 5, G1, G2, –40 forms a geometric progression. If it is possible, state the common ratio; if not, justify why.
(iii) Drawing on your work in parts (i) and (ii), state the general sign conditions on two non–zero real numbers a and b that allow any finite number of real numbers to be inserted between them so that the entire sequence is a geometric progression.