7. [Maximum mark: 7]
A geometric sequence has first term 80 and fourth term 0.74088.
(a) Find the second term. [3]
The first two terms of this geometric sequence are also the first term and eleventh term respectively, of an arithmetic sequence. Let denote the sum of the first terms of the arithmetic sequence.
(b) Find the greatest value of , giving your answer to two decimal places. [4]