The fourth term of a geometric progression is 54 and the tenth term is .

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

Problem

The fourth term of a geometric progression is 54 and the tenth term is

17\,496

. (i) Find the common ratio. (ii) Determine the first term of the progression. (iii) Calculate the value of

\dfrac{a_3\,a_7}{a_5^{\;2}}