If a- a-d- a-2d- is an A-P- then 1-a- 1-a-d- 1-a-2d- is an

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nth Term of an AP

If a, a+d, ...

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If $a, a + d, a + 2 d, . . .$ is an A.P. then $\frac{1}{a}, \frac{1}{a + d}, \frac{1}{a + 2 d}, . . .$ is an

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∣ ∣ ∣ ∣ ∣ ∣ ∣ \begin{matrix} \frac{1}{a} & \frac{1}{a (a + d)} & \frac{1}{(a + d) (a + 2 d)} \frac{1}{(a + d)} & \frac{1}{(a + d) (a + 2 d)} & \frac{1}{(a + 2 d) (a + 3 d)} \frac{1}{(a + 2 d)} & \frac{1}{(a + 2 d) (a + 3 d)} & \frac{1}{(a + 3 d) (a + 4 d)} \end{matrix} ∣ ∣ ∣ ∣ ∣ ∣ ∣

a > 0, d > 0

∣ ∣ ∣ ∣ ∣ ∣ ∣ ∣ ∣ \begin{matrix} \frac{1}{a} & \frac{1}{a (a + d)} & \frac{1}{(a + d) (a + 2 d)} \frac{1}{a (a + d)} & \frac{1}{(a + d) (a + 2 d)} & \frac{1}{(a + 2 d) (a + 3 d)} \frac{1}{(a + 2 d)} & \frac{1}{(a + 2 d) (a + 3 d)} & \frac{1}{(a + 3 d) (a + 4 d)} \end{matrix} ∣ ∣ ∣ ∣ ∣ ∣ ∣ ∣ ∣

\frac{1}{a}, \frac{1}{a + d}, \frac{1}{a + 2 d}, . . .

n^{t h}

a > 0, d > 0.

∣ ∣ ∣ ∣ ∣ ∣ ∣ ∣ ∣ \begin{matrix} \frac{1}{a} & \frac{1}{a (a + d)} & \frac{1}{(a + d) (a + 2 d)} \frac{1}{(a + d)} & \frac{1}{(a + d) (a + 2 d)} & \frac{1}{(a + 2 d) (a + 3 d)} \frac{1}{(a + 2 d)} & \frac{1}{(a + 2 d) (a + 3 d)} & \frac{1}{(a + 3 d) (a + 4 d)} \end{matrix} ∣ ∣ ∣ ∣ ∣ ∣ ∣ ∣ ∣

∣ ∣ ∣ ∣ ∣ \begin{matrix} (a + d) (a + 2 d) & a + 2 d & a 2 d (a + 2 d) & d & d 2 d (a + 3 d) & d & d \end{matrix} ∣ ∣ ∣ ∣ ∣

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