2010 RVHS P1 Q10

Given that the first, third and fourth terms of an arithmetic progression are three consecutive terms of a geometric progression, and that the sum of the first twenty even-numbered terms of the arithmetic progression is \(960\), find the common difference of the arithmetic progression.[4]

Annie puts \(\$\,x\) on 1 January 2010 into a bank account which pays compound interest at a rate of \(3%\) per month on the last day of each month. On the first day of each subsequent month, she puts in an amount which is \(\$\,x\) more than the amount she puts in the previous month. For example, she puts in \(\$\,x\) on 1 January, \(\$\,2x\) on 1 February and so on.