Tag: maths

Questions Related to maths

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

maths numbers and sequences series introduction to series introduction to sequences and series

  1. $9$

  2. $11$

  3. $10$

  4. $8$

Show answer
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

maths numbers and sequences series introduction to series introduction to sequences and series

  1. term

  2. series

  3. constant

  4. sequence

Show answer
Correct Option: B
Explanation:

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

Adding of numbers of some set is called as series.

A _____ is a sum of numbers.

maths numbers and sequences series introduction to series introduction to sequences and series

  1. sequence

  2. series

  3. term

  4. constant

Show answer
Correct Option: B
Explanation:

A series is a sum of numbers.

For example:
$1+3+9+27+....$

What is series?

maths numbers and sequences series introduction to series introduction to sequences and series

  1. adding all the numbers

  2. subtracting all the numbers

  3. multiplying all the numbers

  4. dividing all the numbers

Show answer
Correct Option: A
Explanation:

Series is adding all the numbers or sum of all numbers.

For example: $2+4+6+8+10+....$
This is an AP series with common difference $d=2$.

Which one of the following is not a series?

maths numbers and sequences series introduction to series introduction to sequences and series

  1. adding first $n$ natural numbers

  2. multiplying first $10$ odd numbers

  3. adding first $20$ even numbers

  4. adding last $20$ natural numbers

Show answer
Correct Option: B
Explanation:

A series is the sum of some set of terms of a sequence.
So, multiplying first $10$ odd numbers is not a series.

As it will be equal to $1\times 3\times 5\times 7\times 9....$

$\displaystyle \frac{1}{2}+\frac{1}{4}+\frac{1}{6}+\frac{1}{8}+....$ is a

maths numbers and sequences series introduction to series introduction to sequences and series

  1. sequence

  2. series

  3. term

  4. constant

Show answer
Correct Option: B
Explanation:

$\displaystyle \frac{1}{2}+\frac{1}{4}+\frac{1}{6}+\frac{1}{8}+....$ is a series.

As it shows addition.

Adding and constant difference between the terms is called

maths numbers and sequences series introduction to series introduction to sequences and series

  1. sequence

  2. constant

  3. term

  4. series

Show answer
Correct Option: D
Explanation:

Adding and constant difference between the terms is called series.
Example: $1 + 3 + 5 + 7 +... $
Here the common difference is $2$, adding the terms is called series.

A ______ is the sum of some set of terms of a sequence.

maths numbers and sequences series introduction to series introduction to sequences and series

  1. term

  2. constant

  3. series

  4. sequence

Show answer
Correct Option: C
Explanation:

A series is the sum of some set of terms of a sequence.

For example: 
$2,4,6,8,10,....$
Here it is an series of an A.P. with common difference $d=2$.

Expansion of series: $\displaystyle\sum _{n=0}^4 2n$

maths numbers and sequences series introduction to series introduction to sequences and series

  1. $0+2+4+8+16$

  2. $0+2+4+6+8$

  3. $2+4+6+8+10$

  4. None of the above

Show answer
Correct Option: B
Explanation:

Given:  $\displaystyle\sum _{n=0}^{4} 2n$

At n=0: $2n=2 \times 0=0$
At n=1: $2n=2 \times 1=2$
At n=2: $2n=2 \times 2=4$
At n=3: $2n=2 \times 3=6$
At n=4: $2n=2 \times 4=8$
$\therefore 0+2+4+6+8$

Which of the following is not an example of a series?

maths numbers and sequences series introduction to series introduction to sequences and series

  1. $1,2,3,4,5,6,...$

  2. $-2,0,2,4,6,8,...$

  3. $1,1,2,3,5,8,..$

  4. None of the above

Show answer
Correct Option: D
Explanation:

$(A)$ $1,2,3,4,5,6,....$

This is a arithmetic series with common difference $d=1$

$(B)$ $-2,0,2,4,6,8,...$
This is a arithmetic series with common difference $d=2$

$(C)$ $1,1,2,3,5,8,...$
This is a Fibonacci series in which successive terms is determined by sum of 2 preceding terms.
$a _n=a _{n-1}+a _{n-2}$

Ans: None of the above