Mathematics

Problem

In a positive geometric progression, the third term is

4

and the seventh term is

64

. (i) Establish that the common ratio

r

satisfies the relation

\log_{10} r = \dfrac{\log_{10} 64 - \log_{10} 4}{4}

. (ii) Hence determine the value of

r

. (iii) Find the first term of the progression. (iv) Calculate the sum of the first ten terms of this progression.