Answer
$\approx 8$ years
Work Step by Step
Consider the arithmetic sequence:
$a_1=35,000$
$d=1400$
$S_n=280,000$
Determine the number of years $n$ solving the equation:
$S_n=\dfrac{n(2a_1+(n-1)d)}{2}$
$280,000=\dfrac{n(2(35,000)+(n-1)(1400))}{2}$
$560,000=n(70,000+1400n-1400)$
$560,000=n(1400n+68,000)$
$1400n^2+68,000n-560,000=0$
$200(7n^2+340n-2800)=0$
$7n^2+340n-2800=0$
$n=\dfrac{-340\pm\sqrt{340^2-4(7)(-2800)}}{2(7)}\approx\dfrac{-340\pm 440.45}{14}$
$n_1=\dfrac{-340-440.45}{14}\approx -55.7$
$n_2=\dfrac{-340+440.45}{14}\approx 7.2$
As the number of rows must be a positive integer, the only solution is:
$n\approx 8$ years
