If $a_{1},a_{2},...a_{n}$ are in HP. , Then $\;a_{1}a_{2}+a_{2}a_{3}+.....+a_{n}\;a_{n-1}$ is equal to

Question

$(a)\;n\;(a_{1}-a_{n})\qquad(b)\;(n-1)(a_{1}-a_{n})\qquad(c)\;(n-1)a_{1}a_{n}\qquad(d)\;na_{1}a_{n}$