Question

The first prize in a lottery is $250 000. Each winner chosen after the first is paid 20% as much as the winner before them.
b) Determine an explicit formula for the general term. (2 marks)
c) Determine a formula for the sum of n terms of the geometric sequence. (2 marks)
d) If 5 winning numbers are chosen,
i) how much will the last person chosen be paid? (1 mark)
ii) how much will have been paid out in the lottery?(1 mark)

Answer 1

Clearly, the nth winner gets

250000 * 0.20^(n-1)

This is just a geometric series with

a = 250000
r = 1/5

So, just apply your seies formulas