A robot is stood at its base on mars. It needs to collect samples of dirt and bring them back to base. Each sample lies on the circumference of a circle whose center is the base.

The first sample will be taken from $100\text{m}$ away, and each additional sample will be taken from a further $30\text{m}$ away. The robot can only carry one sample at a time.

The robot can travel a maximum of $10\text{km}$ before it needs to recharge. If it starts with a full battery, how many samples can the robot collect before recharging?

The robot needs to get to each sample and back before going for the next one.

Find a formula, in terms of $n$ where $n$ is the number of complete trips, for the total distance travelled. (You can use $S_n$ for this.)

Try to solve $S_n=10000$ and use the solution to choose the appropriate integer for $n.$