A piece of cord is of length 64 m. It is cut into 16pieces whose lengths are in arithmetic

progression. The length of the longest piece is three times that of the smallest. Find the length of the shortest piece of chord.

$\displaystyle S_n = 64$

length of shortest piece is $\displaystyle x$

length of longest piece is $\displaystyle 3x$

is it right to assume that the shortest piece is the first term and the largest piece is the last term.

is this correct?

i have formed two equations

$\displaystyle 3x = x+(15)d$ equating the longest piece to the last term

$\displaystyle 64 = 16/8 (x + x+15d)$ equating the total length of cord.