(i) Between (-\dfrac{2}{5}) and (\dfrac{2}{13})

Reciprocals: (-\dfrac{5}{2}) and (\dfrac{13}{2}). Insert 5 A.Ms between them (7 terms total).

[ d=\dfrac{\frac{13}{2}-\left(-\frac{5}{2}\right)}{6}=\dfrac{18/2}{6}=\dfrac{9}{6}=\dfrac{3}{2} ]

A.Ms of reciprocals: (-\dfrac{5}{2}+\dfrac{3}{2},; -1+\dfrac{3}{2},;\ldots = -1,;\dfrac{1}{2},; 2,; \dfrac{7}{2},; 5)

H.Ms: (-1,\ 2,\ \dfrac{1}{2},\ \dfrac{2}{7},\ \dfrac{1}{5})

(ii) Between (\dfrac{1}{4}) and (\dfrac{1}{24})

Reciprocals: (4) and (24). (d=\dfrac{20}{6}=\dfrac{10}{3})

A.Ms: (4+\dfrac{10}{3}=\dfrac{22}{3},; \dfrac{32}{3},; 14,; \dfrac{52}{3},; \dfrac{62}{3})

H.Ms: (\dfrac{3}{22},\ \dfrac{3}{32},\ \dfrac{1}{14},\ \dfrac{3}{52},\ \dfrac{3}{62})