(A) The sequence $f(n) = an + b;\, n \in N$ is an $A.P.$By substituting $n = 1, 2, 3, 4, \dots$,we obtain the sequence:$(a + b), (2a + b), (3a + b), \

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(A) The sequence $f(n) = an + b;\, n \in N$ is an $A.P.$By substituting $n = 1, 2, 3, 4, \dots$,we obtain the sequence:$(a + b), (2a + b), (3a + b), \dots$This is an $A.P.$ where the first term $A = (a + b)$ and the common difference $d = a$.Alternatively,the $n^{th}$ term of an $A.P.$ is always of the linear form $an + b$ for all $n \in N$.

Class 11 Mathematics Sequences and Series Arithmetic progression

Easy

Which of the following sequences is an arithmetic sequence?

A
$f(n) = an + b;\, n \in N$
B
$f(n) = k{r^n};\, n \in N$
C
$f(n) = (an + b)k{r^n};\, n \in N$
D
$f(n) = \frac{1}{a(n + \frac{b}{n})};\, n \in N$

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Class 11

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Sequences and Series

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Arithmetic progression

If three positive real numbers $a, b, c$ are in $A$.$P$. and $abc = 4$, then the minimum possible value of $b$ is:

MediumWBJEE 2009

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If the $m^{th}$ terms of the series $63 + 65 + 67 + 69 + \dots$ and $3 + 10 + 17 + 24 + \dots$ are equal,then $m = $

Medium

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Let the six numbers $a_1, a_2, a_3, a_4, a_5, a_6$ be in $A.P.$ and $a_1+a_3=10$. If the mean of these six numbers is $\frac{19}{2}$ and their variance is $\sigma^2$,then $8 \sigma^2$ is equal to

DifficultJEE MAIN 2023

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If $a_1, a_2, a_3, . . . , a_n, . . .$ are in $A.P.$ such that $a_4 - a_7 + a_{10} = m$,then the sum of the first $13$ terms of this $A.P.$ is .............. $m$.

DifficultJEE MAIN 2013

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Let $f: R \rightarrow R$ be such that for all $x \in R$,the terms $(2^{1+x}+2^{1-x})$,$f(x)$,and $(3^x+3^{-x})$ are in $A.P.$. Then the minimum value of $f(x)$ is:

MediumJEE MAIN 2020

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Which of the following sequences is an arithmetic sequence?

Similar Questions

If three positive real numbers $a, b, c$ are in $A$.$P$. and $abc = 4$, then the minimum possible value of $b$ is:

If the $m^{th}$ terms of the series $63 + 65 + 67 + 69 + \dots$ and $3 + 10 + 17 + 24 + \dots$ are equal,then $m = $

Let the six numbers $a_1, a_2, a_3, a_4, a_5, a_6$ be in $A.P.$ and $a_1+a_3=10$. If the mean of these six numbers is $\frac{19}{2}$ and their variance is $\sigma^2$,then $8 \sigma^2$ is equal to

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Let $f: R \rightarrow R$ be such that for all $x \in R$,the terms $(2^{1+x}+2^{1-x})$,$f(x)$,and $(3^x+3^{-x})$ are in $A.P.$. Then the minimum value of $f(x)$ is:

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