Two numbers and are chosen as the first and the last terms of a progression in which…
MATHEMATICS · Multi-part · A Level · Mathematics · Sequences and series · Sequences and series
Problem
Two numbers −8 and 41 are chosen as the first and the last terms of a progression in which exactly two numbers are to be inserted so that the complete sequence is a geometric progression.
(i) Determine the common ratio of the progression.
(ii) Find the two inserted numbers and write the resulting sequence.
(iii) State whether all the terms of this progression are real. Give reason for your answer.