(B) Given the sum of the first $n$ terms $S_n = 5n^2 + 2n$.To find the second term $T_2$,we use the formula $T_2 = S_2 - S_1$.First,calculate $S_1 = 5

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(B) Given the sum of the first $n$ terms $S_n = 5n^2 + 2n$.To find the second term $T_2$,we use the formula $T_2 = S_2 - S_1$.First,calculate $S_1 = 5(1)^2 + 2(1) = 5 + 2 = 7$.Next,calculate $S_2 = 5(2)^2 + 2(2) = 5(4) + 4 = 20 + 4 = 24$.Therefore,$T_2 = S_2 - S_1 = 24 - 7 = 17$.

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

Easy

If the sum of the first $n$ terms of a series is $5n^2 + 2n$,then its second term is

A
$7$
B
$17$
C
$24$
D
$42$

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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

Find the sum to $n$ terms of the series $3 \times 8 + 6 \times 11 + 9 \times 14 + \dots$

Medium

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Easy

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If $f(1)=3$, and $f(n+1)-f(n)=3(4^n-1)$, then for all $n \in N$, $f(n)=$

MediumTS EAMCET 2020

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Let $\{a_{n}\}_{n=0}^{\infty}$ be a sequence such that $a_{0}=a_{1}=0$ and $a_{n+2}=2a_{n+1}-a_{n}+1$ for all $n \geq 0$. Then,$\sum\limits_{n=2}^{\infty} \frac{a_{n}}{7^{n}}$ is equal to

DifficultJEE MAIN 2022

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The sum of the series $3 + 33 + 333 + \dots$ to $n$ terms is

Medium

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If the sum of the first $n$ terms of a series is $5n^2 + 2n$,then its second term is

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