A sequence a1- a2- a3- - an- - - is called arithmetic progression- if difference of the A-P-A- an-an-d- n - NB- an-1-an-d- n - NC- an-1-an-d- n - ND- an-1-an-d- n - N

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Standard X

Mathematics

Sequences, Series and Progressions

A sequence a1...

Question

A sequence a₁, a₂, a₃,…., a_n,…. is called arithmetic progression, if _______ where a₁ is called the first term and the constant term d is called the common difference of the A.P.

a_n = a_n + d, n ЄN

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a_n+1 = a_n + d, n Є N

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a_n+1 = a_n - d, n Є N

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a_n-1 = a_n + d, n Є N

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Solution

The correct option is B
a_n+1 = a_n + d, n Є N

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Similar questions

Q. If

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

is an A.P. with common difference d then

t a n [t a n^{- 1} (\frac{d}{1 + a_{1} a_{2}})] + t a m^{- 1} (\frac{d}{1 + a_{2} a_{3}})] + . . . + t a n^{- 1} (\frac{d}{1 + a_{n - 1} a_{n}})] =

If $a_{1}, a_{2}, a_{3}, \dots, a_{n}$ are in arithmetic progression, where $a_{1} > 0$ for all i.
Prove that $\frac{1}{\sqrt{a_{1}} + \sqrt{a_{2}}} + \frac{1}{\sqrt{a_{2}} + \sqrt{a_{3}}} + \dots + \frac{1}{\sqrt{a_{n - 1}} + \sqrt{a_{n}}} = \frac{n - 1}{\sqrt{a_{1}} + \sqrt{a_{n}}}$

If $a_{1}, a_{2}, a_{3} . . . . . a_{n}$ are in A.P. Where $a_{i} > 0$ for all i, then the value of
$\frac{1}{\sqrt{a_{1}} + \sqrt{a_{2}}} + \frac{1}{\sqrt{a_{2}} + \sqrt{a_{3}}} + . . . . . . . . . + \frac{1}{\sqrt{a_{n - 1}} + \sqrt{a_{n}}} =$

Q. The nth term of an Arithmetic geometric progression is given by

[a + (n - 1) d] b r^{n - 1}

Q. If

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

are first n terms of an A.P. with first term

a_{1} = 0

and common difference

d \neq 0

Then value of

\frac{a_{3} - a_{2}}{a_{2}} + \frac{a_{4} - a_{2}}{a_{3}} + \frac{a_{5} - a_{2}}{a_{4}} . . . . . . . . . . . . \frac{a_{n} - a_{2}}{a_{n - 1}}

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A sequence a1, a2, a3,…., an,…. is called arithmetic progression, if _______ where a1 is called the first term and the constant term d is called the common difference of the A.P.

The correct option is B an+1 = an + d, n Є N

A sequence a₁, a₂, a₃,…., a_n,…. is called arithmetic progression, if _______ where a₁ is called the first term and the constant term d is called the common difference of the A.P.

The correct option is B
a_n+1 = a_n + d, n Є N