Mathematics

The key is to set up an equation using the sum formula for an arithmetic progression. You know the sum of the first $n$ terms ($S_n = \frac{n}{2}(2a + (n-1)d)$) and the $n$th term ($a_n = a + (n-1)d$), so translate "sum equals four times the $n$th term" into an equation and solve for $n$. Simplifying will give you a linear equation in $n$.

The key is to set up an equation using the sum formula for an arithmetic progression. You know the sum of the first $n$ terms ($S_n = \frac{n}{2}(2a + (n-1)d)$) and the $n$th term ($a_n = a + (n-1)d$), so translate "sum equals four times the $n$th term" into an equation and solve for $n$. Simplifying will give you a linear equation in $n$.