Tag: series

Questions Related to series

When each term of a sequence is connected using $a +$ or $a -$ sign, then it is referred to as the _____ of numbers.

  1. Series

  2. Progression

  3. Arithmetic Progression

  4. Geometric Prpgression


Correct Option: A
Explanation:

When each term of a sequence is connected using a $+$ or a $-$ sign, then it is referred to as the series of numbers. For example, $2 + 5 + 8 + 11 + 15 + 18 + ....$ is a series of numbers. Thus the correct answer is '$a$'.

In following symbol series, some of the symbols are missing which are given in that order as one of the alternatives below it. Choose the correct alternative.

$\text{x+ _ xx _+++ _ xxx _ +++x}$

  1. $\text{x++x}$

  2. $\text{+xx+}$

  3. $\text{xxx+}$

  4. $\text{x+x+}$

  5. $\text{x+xx}$


Correct Option: B
Explanation:

The series is $\text{x++/xxx+++/ xxxx++++/x}$. Thus, the letters are repeated twice, thrice and so on.

Hence, the missing symbols are +xx+

Adding all the terms in a sequence is called

  1. sequence

  2. series

  3. term

  4. constant


Correct Option: B
Explanation:

Adding all the terms in a sequence is called series.
Example: 1 + 2 + 3 + 4 is a series.

$1 + 2 + 3 + 4 + 5 +.....$ is a

  1. sequence

  2. term

  3. constant

  4. series


Correct Option: D
Explanation:

$1 + 2 + 3 + 4 + 5 +.....$ is a series.
As sum of all numbers in some set is called as a series.

A sum of an infinite sequence it is called a

  1. term

  2. constant

  3. series

  4. sequence


Correct Option: C
Explanation:

A sum of an infinite sequence it is called a series.
Example: $2 + 4 + 6 + 8 +....$ is a series.

Which one of the following is a series?

  1. $1 \times  2 \times  3 \times  4 \times  5$

  2. $(0, 1, 2, 3, 4)$

  3. $\left {1, 2, 3, 5, 6\right }$

  4. $\sum _{n=1}^{10}nk^2$


Correct Option: D
Explanation:

$\sum _{n=1}^{10}nk^2$ is a series.
Since $\sum _{n=1}^{10}nk^2= k^2+2k^2+3k^2+4k^2+5k^2+6k^2+7k^2+8k^2+9k^2+10k^2$
So, sum of all the terms in a sequence is called series.

Identify the series.

  1. {$1, 2, 3, 4, 5$}

  2. $1 + 2 + 3 + 4 + 5$

  3. $1 \times  2 \times  3 \times  4$

  4. $2 - 4 \times  3 + 1 - 23$


Correct Option: B
Explanation:

$1 + 2 + 3 + 4 + 5$ is a series.

Rest all are not series.
Series means sum of all numbers in a set.

The sum of first $5$ odd numbers is called

  1. term

  2. constant

  3. series

  4. sequence


Correct Option: C
Explanation:

The sum of first $5$ odd numbers is called series.
Example: $1 + 3 + 5 + 7 + 9 $ is a series.

What is the next term of the series $1 + 3 + 5 + 7 +$ ___?

  1. $9$

  2. $11$

  3. $10$

  4. $8$


Correct Option: A
Explanation:

Given series is $1 + 3 + 5 + 7 $ _

The next term of the series will be $9$, as the common difference is $2$.
Hence, the series is $1+3+5+7+9+$ _
.

Adding first $100$ terms in a sequence is called

  1. term

  2. series

  3. constant

  4. sequence


Correct Option: B
Explanation:

Adding first $100$ terms in a sequence is called series.

Adding of numbers of some set is called as series.