If A1- A2- A3- - An are n numbers between a and b- such that a- A1- A2- A3- - An- b are in A-P- thenA- A1- A2- A3- - An are arithmetic means between a and bB- A1- A2- A3- - - An are in harmonic progressionC- A 1- A 2- A 3- - A n are in geometric progressionD- A1- A2- A3- - An all are equal

The correct option is A A1, A2, A3,...., An are arithmetic means between a and b If A1, A2, A3,..., An are n numbers between a and b, such that a, A1, A2 ...

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Standard X

Mathematics

Sequences, Series and Progressions

If A1, A2, A3...

Question

If A₁, A₂, A₃,..., A_n are n numbers between a and b, such that a, A₁, A₂, A₃,..., A_n, b are in A.P., then

A₁, A₂, A₃,...., A_n are arithmetic means between a and b

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A₁, A₂, A₃,....., A_n are in harmonic progression

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A₁, A₂, A₃,...., A_n all are equal

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A₁, A₂, A₃,....., A_n are in geometric progression

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Solution

The correct option is A
A₁, A₂, A₃,...., A_n are arithmetic means between a and b

If A₁, A₂, A₃,..., A_n are n numbers between a and b, such that a, A₁, A₂, A₃,..., A_n, b are in A.P., then A₁, A₂, A₃,...., A_n are arithmetic means between a and b.

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Similar questions

Q. If

A_{1}, A_{2}, A_{3}, . . . A_{n}

are

n

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and

b

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a, A_{1}, A_{2}, . . . ., A_{n}, b

is an A.P., then

A_{1} + A_{2} + A_{3} . . . A_{n}

Q. If

a_{1}, a_{2}, a_{3}, . . . a_{n}

are in H.P then

\frac{a_{1}}{a_{2} + a_{3} + . . . a_{n}}, \frac{a_{2}}{a_{1} + a_{3} + . . . a_{n}}, \frac{a_{3}}{a_{1} + a_{2} + a_{4} + . . . + a_{n}}, \frac{a_{n}}{a_{1} + a_{2} + . . . + a_{n}}

are in

Q. If

a_{1}, a_{2}, a_{3}, . . . . a_{n}

are in H.P, then

\frac{a_{1}}{a_{2} + a_{3} + . . . . + a_{n}}, \frac{a_{2}}{a_{1} + a_{3} + . . . . + a_{n}}, . . . ., \frac{a_{n}}{a_{1} + a_{2} + . . . . + a_{n - 1}}

are in

Q. If

a_{1}, a_{2}, a_{3}, . . . . . a_{n}

are in H.P., then

\frac{a_{1}}{a_{2} + a_{3} + . . . a_{n}}, \frac{a_{2}}{a_{1} + a_{3} + . . . . + a_{n}}, \frac{a_{n}}{a_{1} + a_{2} + . . . + a_{n - 1}}

are in

Q. If

a_{1}, a_{2}, a_{3}, . . . . ., a_{n}

are in H.P. then prove that

\frac{a_{1}}{a_{2} + a_{3} + . . . a_{n}}, \frac{a_{2}}{a_{2} + a_{3} + . . . a_{n}}, \frac{a_{3}}{a_{2} + a_{3} + . . . a_{n}}

are in H.P.

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If A1, A2, A3,..., An are n numbers between a and b, such that a, A1, A2, A3,..., An, b are in A.P., then

The correct option is A A1, A2, A3,...., An are arithmetic means between a and b If A1, A2, A3,..., An are n numbers between a and b, such that a, A1, A2, A3,..., An, b are in A.P., then A1, A2, A3,...., An are arithmetic means between a and b.

If A₁, A₂, A₃,..., A_n are n numbers between a and b, such that a, A₁, A₂, A₃,..., A_n, b are in A.P., then

The correct option is A
A₁, A₂, A₃,...., A_n are arithmetic means between a and b

If A₁, A₂, A₃,..., A_n are n numbers between a and b, such that a, A₁, A₂, A₃,..., A_n, b are in A.P., then A₁, A₂, A₃,...., A_n are arithmetic means between a and b.