Harmonic Progression

Q.

If a, b, c, are in H.P. then

1. All are correct

2. $\frac{b+a}{b-a}+\frac{b+c}{b-c}=2$

3. $\frac{a-b}{b-c}=\frac{a}{c}$

4. $\frac{1}{b-a}+\frac{1}{b-c}=\frac{1}{a}+\frac{1}{c}$

Q. If $a_1,a_2,a_3,\dots \dots$ are in a harmonic progression with $a_1=5$ and $a_{20}=25$. Then, the least positive integer n for which $a_n<0$, is

1. 22
2. 24
3. 25
4. 23

Q. 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 AP
and |a| <1, |b|<1, |c|<1 then x, y, z are in

1. GP
2. AP
3. Arithmetic- Geometric progression
4. H.P

Q. Let $a_1,a_2,a_3.$..... be in harmonic progression with $a_1=5$ and $a_{20}=25$. The least positive integer n for which $a_n<0$ is

1. 25
2. 22
3. 23
4. 24

Q. If a, b, c, d are in H.P. , then ab +bc+cd =

1. ad
2. 2ad
3. 3ad
4. 4ad

Q.

If ln(a+c) , ln(a-c) , ln(a-2b+c) are in A.P, then

1. a, b, c are in A.P.

2. $a^2,b^2,c^2$ are in A.P.

3. a, b, c are in H.P.

4. a, b, c are in G.P.

Q.

If the roots of $a(b-c)x^2+b(c-a)x+c(a-b)$ = 0 be equal then a, b, c are in

1. A.P

2. G.P

3. H.P

4. None of these

Q.

If a, b, c, d are in H.P., then ab + bc + cd is equal to

1. 3ad

2. 3ac

3. None of these

4. 

Q.

If a, b, c are in H.P then $4^{-a},4^{-b},4^{-c}$ are in

1. A.P
2. G.P
3. H.P
4. none of these

Q.

If $\frac{1}{b-a}+\frac{1}{b-c}=\frac{1}{a}+\frac{1}{c},$ then a, b, c, are in

1. A.P
2. G.P
3. H.P
4. none of these