9.
The first term of a geometric progression is 10 and the common ratio is 0.8 .
- Find the fourth term.
- Find the sum of the first 20 terms, giving your answer correct to 3 significant figures.
- The sum of the first \(N\) terms is denoted by \(S _ { N }\), and the sum to infinity is denoted by \(S _ { \infty }\). Show that the inequality \(S _ { \infty } - S _ { N } < 0.01\) can be written as
$$0.8 ^ { N } < 0.0002$$
and use logarithms to find the smallest possible value of \(N\).
[0pt]
[BLANK PAGE]