(A) The sum of $n$ terms of an arithmetic progression is given by $S_n = \frac{n}{2}[2a + (n - 1)d]$.For the numerator: $a = 3, d = 2$. Sum $= \frac{n

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(A) The sum of $n$ terms of an arithmetic progression is given by $S_n = \frac{n}{2}[2a + (n - 1)d]$.For the numerator: $a = 3, d = 2$. Sum $= \frac{n}{2}[6 + (n - 1)2] = \frac{n}{2}[2n + 4] = n(n + 2)$.For the denominator: $10$ terms,$a = 5, d = 3$. Sum $= \frac{10}{2}[2(5) + (10 - 1)3] = 5[10 + 27] = 5 \times 37 = 185$.Given $\frac{n(n + 2)}{185} = 7$.$n^2 + 2n = 1295$.$n^2 + 2n - 1295 = 0$.$(n + 37)(n - 35) = 0$.Since $n$ must be positive,$n = 35$.

Class 11 Mathematics Sequences and Series Arithmetic progression

Easy

If $\frac{3 + 5 + 7 + \dots + (2n + 1)}{5 + 8 + 11 + \dots + (3n + 2)} = 7$,find the value of $n$. (Note: The original problem implies $n$ terms in the numerator and $10$ terms in the denominator as per the provided solution structure).

A
$35$
B
$36$
C
$37$
D
$40$

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Class 11

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Sequences and Series

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Arithmetic progression

$A$ farmer buys a used tractor for $Rs. 12000$. He pays $Rs. 6000$ cash and agrees to pay the balance in annual instalments of $Rs. 500$ plus $12\%$ interest on the unpaid amount. How much will the tractor cost him?

Difficult

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Let $S_n$ denote the sum of the first $n$ terms of an arithmetic progression. If $S_{10} = 390$ and the ratio of the tenth and the fifth terms is $15:7$,then $S_{15} - S_5$ is equal to:

DifficultJEE MAIN 2024

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If the ratio of the sum of $n$ terms of two $A.P.s$ is $(7n + 1):(4n + 27)$,then the ratio of their $11^{th}$ terms is:

Medium

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If $x, y, z$ are in an arithmetic progression,and $a$ is the arithmetic mean of $x$ and $y$,and $b$ is the arithmetic mean of $y$ and $z$,then what is the arithmetic mean of $a$ and $b$?

Easy

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If $a_1, a_2, a_3, \dots$ are in $A.P.$ such that $a_1 + a_7 + a_{16} = 40$,then the sum of the first $15$ terms of this $A.P.$ is

DifficultJEE MAIN 2019

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If $\frac{3 + 5 + 7 + \dots + (2n + 1)}{5 + 8 + 11 + \dots + (3n + 2)} = 7$,find the value of $n$. (Note: The original problem implies $n$ terms in the numerator and $10$ terms in the denominator as per the provided solution structure).

Similar Questions

$A$ farmer buys a used tractor for $Rs. 12000$. He pays $Rs. 6000$ cash and agrees to pay the balance in annual instalments of $Rs. 500$ plus $12\%$ interest on the unpaid amount. How much will the tractor cost him?

Let $S_n$ denote the sum of the first $n$ terms of an arithmetic progression. If $S_{10} = 390$ and the ratio of the tenth and the fifth terms is $15:7$,then $S_{15} - S_5$ is equal to:

If the ratio of the sum of $n$ terms of two $A.P.s$ is $(7n + 1):(4n + 27)$,then the ratio of their $11^{th}$ terms is:

If $x, y, z$ are in an arithmetic progression,and $a$ is the arithmetic mean of $x$ and $y$,and $b$ is the arithmetic mean of $y$ and $z$,then what is the arithmetic mean of $a$ and $b$?

If $a_1, a_2, a_3, \dots$ are in $A.P.$ such that $a_1 + a_7 + a_{16} = 40$,then the sum of the first $15$ terms of this $A.P.$ is

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