The first three terms of a sequence are (in the stated order)

MATHEMATICS · Multi-part · A Level · Mathematics · Sequences and series · Sequences and series

Problem

The first three terms of a sequence are

k-1,\;2,\;k+3

(in the stated order). Suppose these three numbers are consecutive terms of a geometric progression. (i) Determine all possible value(s) of

k

. (ii) For each admissible value of

k

, find the common ratio. (iii) Using that ratio, compute the sum of the first six terms of the progression.