Finite Series

Some quantities arranged in a particular way such that antecedent and subsequent terms become related — the arrangement is called —

The number of terms of any sequence is —

The set $\{2, 4, 6, \ldots\}$ is the set of —

If $f(n) = 2n$, then $f(5) = ?$

The first term of the sequence $1, 3, 5, 7, \ldots$ is —

The general term of the sequence $1, 4, 9, 16, \ldots$ is —

The first term of the sequence $\left\{\dfrac{n-1}{n+1}\right\}$ is —

The third term of the sequence $\left\{\dfrac{1}{n}\right\}$ is —

The second term of the sequence $\left\{\dfrac{n}{n+1}\right\}$ is —

If $f(n) = 2n + 1$, the third term of the sequence is —

The general term of the sequence $\dfrac{1}{2}, \dfrac{2}{3}, \dfrac{3}{4}, \ldots$ is —

The fourth term of the sequence $\{n^{2}\}$ is —

If the terms of a sequence are connected successively by the $+$ sign, the result is called —

In the series $1 + 3 + 5 + 7 + \cdots$, the differences between successive terms are —

In the series $2 + 4 + 8 + 16 + \cdots$, the ratios of successive terms are —

A series with a fixed (countable) number of terms is called —

A series whose terms do not end is called —

In an arithmetic series, the difference between any two adjacent terms is —

The common difference of the series $1 + 3 + 5 + 7 + 9 + 11$ is —

In an arithmetic series the first term is generally denoted by —

The common difference of an arithmetic series is generally denoted by —

An arithmetic series with first term $a$ and common difference $d$ is —

The common difference of $7 + 13 + 19 + 25 + \cdots$ is —

The common difference of $2, -5, -12, -19, \ldots$ is —

The common difference of $29 + 25 + 21 + \cdots$ is —

The common difference of $5 + 8 + 11 + 14 + \cdots + 62$ is —

The series $1 + 4 + 7 + 10 + \cdots$ is —

Which of the following is an arithmetic series?

The $n$-th term of an arithmetic series with first term $a$ and common difference $d$ is —

If $a = 3$ and $d = 2$, the $n$-th term of the arithmetic series is —

The $n$-th term of $5 + 8 + 11 + 14 + \cdots$ is —

The $n$-th term of $13 + 20 + 27 + 34 + \cdots$ is —

The $n$-th term of $7 + 13 + 19 + 25 + \cdots$ is —

The $n$-th term of $8 + 11 + 14 + 17 + \cdots$ is —

The $n$-th term of $4 + 7 + 10 + 13 + \cdots$ is —

The $15$th term of $7 + 13 + 19 + 25 + \cdots$ is —

The number of terms of the series $13 + 20 + 27 + 34 + \cdots + 111$ is —

Which term of the series $8 + 11 + 14 + 17 + \cdots$ is $392$?

Which term of the series $4 + 7 + 10 + 13 + \cdots$ is $301$?

Which term of the series $5 + 8 + 11 + \cdots$ is $383$?

The $12$th term of the series $2, -5, -12, -19, \ldots$ is —

If $a = 5$ and $d = 7$, the $(2p+1)$th term of the arithmetic series is —

If the $m$-th term of an arithmetic series is $n$ and the $n$-th term is $m$, the $(m+n)$th term is —

The $22$nd term of the arithmetic series with $a = 5$ and $d = 7$ is —

The $19$th term of the series $5 + 8 + 11 + 14 + \cdots + 62$ is —

If first term $a$, last term $p$ and number of terms $n$ are known, the sum of an arithmetic series is —

If first term $a$, common difference $d$ and number of terms $n$ are known, the sum is —

The sum of the first $50$ natural numbers is —

$1 + 2 + 3 + \cdots + 99 = ?$

The sum of the first $30$ terms of $7 + 12 + 17 + \cdots$ is —

The sum of the first $20$ terms of $7 + 13 + 19 + 25 + \cdots$ is —

The sum of the first $n$ terms of $1 + 3 + 5 + 7 + \cdots$ is —

The sum of the first $9$ terms of $8 + 16 + 24 + \cdots$ is —

$5 + 11 + 17 + 23 + \cdots + 59 = ?$

$29 + 25 + 21 + \cdots + (-23) = ?$

If the $12$th term of an arithmetic series is $77$, the sum of the first $23$ terms is —

If the $16$th term of an arithmetic series is $-20$, the sum of the first $31$ terms is —

The sum of the first $n$ terms of $9 + 7 + 5 + \cdots$ is $-144$. The value of $n$ is —

The sum of the first $n$ terms of $2 + 4 + 6 + 8 + \cdots$ is $2550$. The value of $n$ is —

If the sum of the first $n$ terms of a series is $n(n + 1)$, the series is —

If the sum of the first $n$ terms of a series is $n(n + 1)$, the sum of the first $10$ terms is —

If the sum of the first $12$ terms of an arithmetic series is $144$ and the sum of the first $20$ terms is $560$, the sum of the first $6$ terms is —

If the sum of the first $m$ terms of an arithmetic series is $n$ and the sum of the first $n$ terms is $m$, the sum of the first $(m + n)$ terms is —

$1 + 2 + 3 + \cdots + n = ?$

$1^{2} + 2^{2} + 3^{2} + \cdots + n^{2} = ?$

$1^{3} + 2^{3} + 3^{3} + \cdots + n^{3} = ?$

$1 + 2 + 3 + \cdots + 10 = ?$

$1^{2} + 2^{2} + \cdots + 10^{2} = ?$

$1^{3} + 2^{3} + \cdots + 10^{3} = ?$

$\left(1 + 2 + 3 + \cdots + n\right)^{2} = ?$

$8^{2} + 9^{2} + 10^{2} + \cdots + 15^{2} = ?$

If $\dfrac{1^{3} + 2^{3} + 3^{3} + \cdots + n^{3}}{1 + 2 + 3 + \cdots + n} = 210$, the value of $n$ is —

If the sum of the cubes of the first $n$ natural numbers is $441$, the value of $n$ is —

If the sum of the cubes of the first $n$ natural numbers is $441$, the value of $1 + 2 + 3 + \cdots + n$ is —

The sum of the first $n$ natural even numbers is —

The sum of the squares of the first $n$ natural odd numbers is —

$1 + 2 + 3 + \cdots + 100 = ?$

$1^{2} + 2^{2} + \cdots + 100^{2} = ?$

$1^{3} + 2^{3} + \cdots + 100^{3} = ?$

Rashid deposits Tk. $1200$ in the first month and Tk. $100$ more each subsequent month. The series of his deposits is —

Rashid deposits Tk. $1200$ in the first month with Tk. $100$ monthly increment. His deposit in the $18$th month is (Tk.) —

Rashid's total deposit in the first $18$ months is (Tk.) —

The number of months Rashid takes to deposit a total of Tk. $106200$ is —

The time Rashid takes to deposit Tk. $106200$ is —

A man repays a loan of Tk. $2500$ in installments. The first installment is Tk. $1$ and each later installment is Tk. $2$ more than the previous. The number of installments is —

Palash's basic salary starts at Tk. $120000$ per year with yearly increment Tk. $5000$. His salary forms —

After $10\%$ deduction for provident fund, the first three terms of Palash's net salary series are —

The common difference of Palash's net salary series after $10\%$ PF deduction is —

Palash's total net salary over $26$ years (excluding PF) is (Tk.) —

A student saves Tk. $10$ in the first week and increases the saving by Tk. $5$ each subsequent week. Total savings after $20$ weeks (Tk.) —

If the ratio of any term to its antecedent term in a series is always equal, the series is called —

In a geometric series, the constant ratio is called —

The first term of a geometric series is generally denoted by —

The common ratio of a geometric series is generally denoted by —

A geometric series with first term $a$ and common ratio $r$ is —

The common ratio of $2 + 4 + 8 + 16 + 32$ is —

The common ratio of $128 + 64 + 32 + \cdots$ is —

The common ratio of $3 + 9 + 27 + 81 + \cdots$ is —

The common ratio of $1 + \dfrac{1}{2} + \dfrac{1}{4} + \dfrac{1}{8} + \cdots$ is —