(D) Given the recurrence relation: $a_{n+1} - a_n = n - 2$. Summing this from $n = 1$ to $50$: $\sum_{n=1}^{50} (a_{n+1} - a_n) = \sum_{n=1}^{50} (n -

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(D) Given the recurrence relation: $a_{n+1} - a_n = n - 2$. Summing this from $n = 1$ to $50$: $\sum_{n=1}^{50} (a_{n+1} - a_n) = \sum_{n=1}^{50} (n - 2)$ $a_{51} - a_1 = \sum_{n=1}^{50} n - \sum_{n=1}^{50} 2$ $a_{51} - 5 = \frac{50 \times 51}{2} - (50 \times 2)$ $a_{51} - 5 = 1275 - 100$ $a_{51} - 5 = 1175$ $a_{51} = 1180$.

Class 11 Mathematics Sequences and Series nth term of special series, Sum to n terms and Infinite number of terms

Let $a_n$ be a sequence such that $a_1 = 5$ and $a_{n+1} = a_n + (n - 2)$ for all $n \in N$. Then $a_{51}$ is:

A
$1165$
B
$1170$
C
$1175$
D
$1180$

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Class 11

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Sequences and Series

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nth term of special series, Sum to n terms and Infinite number of terms

The sum of the first $9$ terms of the series $\frac{1^3}{1} + \frac{1^3 + 2^3}{1 + 3} + \frac{1^3 + 2^3 + 3^3}{1 + 3 + 5} + \dots$ is:

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The sum of all the products of the first $n$ natural numbers taken two at a time is

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What is the sum of the first $10$ terms of the series $0.7 + 0.77 + 0.777 + \dots$?

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For a series whose $n^{th}$ term is $\left( \frac{n}{x} \right) + y$,the sum of $r$ terms is:

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If $S_n$ is the sum of the first $n$ terms of the series $1^2+2 \times 2^2+3^2+2 \times 4^2+5^2+2 \times 6^2+\ldots$,then for even $n$,$S_n$ is equal to:

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Let $a_n$ be a sequence such that $a_1 = 5$ and $a_{n+1} = a_n + (n - 2)$ for all $n \in N$. Then $a_{51}$ is:

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The sum of the first $9$ terms of the series $\frac{1^3}{1} + \frac{1^3 + 2^3}{1 + 3} + \frac{1^3 + 2^3 + 3^3}{1 + 3 + 5} + \dots$ is:

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