Given that the first, third and fourth terms of an arithmetic progression are three consecutive term

Question

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. Show that the amount of money in the bank account on the last day of March is $\$\frac{103x}{9}\left[103{{\left(1.03\right)}^{3}}-112\right]$. [4] Find the least integer value of $x$ so that the amount of interest earned for the first three months of the year 2010 exceeds $\$100$. [2]

Accepted Answer

$329$

2010 RVHS P1 Q10

2010 RVHS P1 Q10

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