Harmonic Progression (H.P.)

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If $a_{1}, a_{2}, \dots, a_{n}$ are in H.P., then the expression $a_{1} a_{2} + a_{2} a_{3} + \dots + a_{n - 1} a_{n}$ is equal to

n (a_{1} - a_{n})

(n - 1) (a_{1} - a_{n})

n a_{1} a_{n}

(n - 1) a_{1} a_{n}

If $x = \sum_{n = 0}^{\infty} a^{n}, y = \sum_{n = 0}^{\infty} b^{n}, z = \sum_{n = 0}^{\infty} c^{n}$ where $a, b, c$ are in A.P and $∣ a ∣ < 1, ∣ b ∣ < 1, ∣ c ∣ < 1$ then $x, y, z$ are in

Arithmetic - Geometric Progression

LEVELJEE Advanced

Let $R_{1}$ and $R_{2}$ respectively be the maximum ranges up and down an inclined plane and $R$ be the maximum range on the horizontal plane. Then $R_{1}, R, R_{2}$ are in

JEE Advanced 2012

Let $a_{1}, a_{2}, a_{3} \dots$ be in harmonic progression with $a_{1} = 5$ and $a_{20} = 25$ . The least positive integer $n$ for which $a_{n} < 0$ is

JEE Advanced 2001

Let the positive numbers $a, b, c, d$ be in A.P. Then $ab c, ab d, a c d, b c d$ are

NOT in A.P./G.P./H.P.

JEE Advanced 1999

Let $a_{1}, a_{2}, \dots, a_{10}$ be in A.P. and $h_{1}, h_{2}, \dots, h_{10}$ be in H.P. If $a_{1} = h_{1} = 2$ and $a_{10} = h_{10} = 3$ , then $a_{4} h_{7}$ is

JEE Advanced 1998

If $x > 1, y > 1, z > 1$ are in G.P., then $\frac{1}{1 + l n x}, \frac{1}{1 + l n y}, \frac{1}{1 + l n z}$ are in

JEE Main 2018 (16 April Shift 1)

Let $\frac{1}{x _{1}}, \frac{1}{x _{2}}, \dots, \frac{1}{x _{n}}$ ( $x_{i} \neq = 0$ for $i = 1, 2, \dots, n$ ) be in A.P. such that $x_{1} = 4$ and $x_{21} = 20$ . If n is the least positive integer for which $x_{n} > 50$ , then $\sum_{i = 1}^{n} (\frac{1}{x _{i}})$ is equal to :

\frac{1}{8}

\frac{13}{8}

\frac{13}{4}