Tag: numbers and sequences

Questions Related to numbers and sequences

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

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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

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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

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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

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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

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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

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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

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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

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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

A fibonacci series is:

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

  1. series of numbers in which each number (Fibonacci number) is the sum of the two preceding numbers.

  2. the simplest is the series $1, 1, 2, 3, 5, 8,$ etc.

  3. Both are correct

  4. None is correct

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Correct Option: C
Explanation:
Sol: A Fibonacci series of numbers is in which each number is the sum of the two preceding numbers examples,
$1,1,2,3,5,8$----------

Which of the following is not a series?

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

  1. AP

  2. GP

  3. Fibonacci pattern

  4. None of the above

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Correct Option: D
Explanation:

Arithmetic progression, Geometric progression and Fibonacci pattern are all series.