(D) Given the sum of $n$ terms is $S_n = nA + n^2B$.For $n = 1$,$S_1 = A(1) + B(1)^2 = A + B$. Thus,the first term $a = S_1 = A + B$.For $n = 2$,$S_2

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(D) Given the sum of $n$ terms is $S_n = nA + n^2B$.For $n = 1$,$S_1 = A(1) + B(1)^2 = A + B$. Thus,the first term $a = S_1 = A + B$.For $n = 2$,$S_2 = A(2) + B(2)^2 = 2A + 4B$.The second term $a_2 = S_2 - S_1 = (2A + 4B) - (A + B) = A + 3B$.The common difference $d = a_2 - a = (A + 3B) - (A + B) = 2B$.

Class 11 Mathematics Sequences and Series Arithmetic progression

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The sum of $n$ terms of an arithmetic progression is $nA + n^2B$,where $A$ and $B$ are constants. The common difference of this progression is.......

A
$A - B$
B
$A + B$
C
$2A$
D
$2B$

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Class 11 Questions

Class 11

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Sequences and Series

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Arithmetic progression

The sum of $n$ arithmetic means between $a$ and $b$ is:

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If the sum of three numbers in an $A.P.$ is $24$ and their product is $440,$ find the numbers.

Medium

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Let $S_n$ be the sum of the first $n$ terms of an arithmetic progression $3, 7, 11, \ldots$. If $40 < \left(\frac{6}{n(n+1)} \sum_{k=1}^{n} S_{k}\right) < 42$,then $n$ equals

DifficultJEE MAIN 2024

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Which of the following sequences is an arithmetic sequence?

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Let $a_n$ be the $n^{\text{th}}$ term of an $A.P.$ If $S_n = a_1 + a_2 + a_3 + \dots + a_n = 700$,$a_6 = 7$,and $S_7 = 7$,then $a_n$ is equal to:

DifficultJEE MAIN 2025

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The sum of $n$ terms of an arithmetic progression is $nA + n^2B$,where $A$ and $B$ are constants. The common difference of this progression is.......

Similar Questions

The sum of $n$ arithmetic means between $a$ and $b$ is:

If the sum of three numbers in an $A.P.$ is $24$ and their product is $440,$ find the numbers.

Let $S_n$ be the sum of the first $n$ terms of an arithmetic progression $3, 7, 11, \ldots$. If $40 < \left(\frac{6}{n(n+1)} \sum_{k=1}^{n} S_{k}\right) < 42$,then $n$ equals

Which of the following sequences is an arithmetic sequence?

Let $a_n$ be the $n^{\text{th}}$ term of an $A.P.$ If $S_n = a_1 + a_2 + a_3 + \dots + a_n = 700$,$a_6 = 7$,and $S_7 = 7$,then $a_n$ is equal to:

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