6 Sarah is carrying out a series of experiments which involve using increasing amounts of a chemical. In the first experiment she uses 6 g of the chemical and in the second experiment she uses 7.8 g of the chemical.
- Given that the amounts of the chemical used form an arithmetic progression, find the total amount of chemical used in the first 30 experiments.
- Instead it is given that the amounts of the chemical used form a geometric progression. Sarah has a total of 1800 g of the chemical available. Show that \(N\), the greatest number of experiments possible, satisfies the inequality
$$1.3 ^ { N } \leqslant 91 ,$$
and use logarithms to calculate the value of \(N\).