$\displaystyle \text{A piece of cord is of length 64 m.}$

$\displaystyle \text{It is cut into 16 pieces whose lengths are in arithmetic progression.}$

$\displaystyle \text{The length of the longest piece is three times that of the smallest.}$

$\displaystyle \text{Find the length of the shortest piece of cord.}$

$\displaystyle S_n = 64$

$\displaystyle \text{length of shortest piece is }x$

$\displaystyle \text{length of longest piece is }3x$

$\displaystyle \text{Is it right to assume that the shortest piece is the first term}$

. . $\displaystyle \text{and the largest piece is the last term?}$

$\displaystyle \text{i have formed two equations:}$

$\displaystyle 3x \:=\: x+(15)d\qquad \text{equating the longest piece to the last term}$

$\displaystyle 64 \:= \frac{16}{2}(2x +15d) \qquad\text{equating the total length of cord}$