Tag: maths

Quizzes (518) Questions (9324)

Questions Related to maths

Multiple choice maths geometric sequences introduction to geometric progression understanding geometric progressions introduction to geometric progressions

A sequence of numbers such that the quotient of any two successive members of the sequence is a constant called the common ratio of the sequence is known as:

  1. geometric series

  2. arithmetic progression

  3. harmonic sequence

  4. geometric sequence
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

A sequence of number, ${ a } _{ 1 }+{ a } _{ 2 }+......{ a } _{ n }$ quotient of any two successive number is a constant,

$\cfrac { { a } _{ 2 } }{ { a } _{ 1 } } =\cfrac { { a } _{ 3 } }{ { a } _{ 2 } } =........=\cfrac { { a } _{ n } }{ { a } _{ n-1 } } =$common ratio $(r)$
So we can write
${ a } _{ 1 }+{ a } _{ 1 }r+{ a } _{ 2 }r+{ a } _{ 3 }r.......{ a } _{ n-1 }r\ ={ a } _{ 1 }+{ a } _{ 1 }r+{ a } _{ 1 }{ r }^{ 2 }..........{ a } _{ n-2 }{ r }^{ 2 }$
and in the end in terms of ${ a } _{ 1 }$
$={ a } _{ 1 }+{ a } _{ 1 }r+{ a } _{ 1 }{ r }^{ 2 }+{ a } _{ 1 }{ r }^{ 3 }.........{ a } _{ 1 }{ r }^{ n-1 }$
We can clearly say this series is in $GP$.
Answer $(D)$

Multiple choice maths geometric sequences introduction to geometric progression understanding geometric progressions introduction to geometric progressions

Which one of the following is not a geometric progression?

  1. $1, 2, 4, 8, 16, 32$
  2. $4, -4, 4, -4, 4$
  3. $12, 24, 36, 48$
  4. $6, 12, 24, 48$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation
For geometric progression, the ratio of the consecutive terms should be equal.
Here $12, 24, 36, 48$ is not a geometric progression. Here only the difference is common i.e. $12$.
Rest all options have same common ratio i.e., in option A, the ratio is $2$. In option B, the ratio is $-1$.
And in option D, the ratio is $2$.
Here the given sequence is an arithmetic progression.
Multiple choice maths geometric sequences introduction to geometric progression understanding geometric progressions introduction to geometric progressions

Which of the following is not in the form of G.P.?

  1. $2 + 6 + 18 + 54 +...$
  2. $3 + 12 + 48 + 192 +....$
  3. $1 + 4 + 7 + 10 +....$
  4. $1 + 3 + 9 + 27 +....$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

In option A, the common ratio is $3$.
In option B, the common ratio is $4$.
In option D, the common ratio is $3$.
$1 + 4 + 7 + 10 +...$. is not a G.P., since the sequence is in the form of A.P.

Multiple choice maths geometric sequences introduction to geometric progression understanding geometric progressions introduction to geometric progressions

Which one of the following is a general form of geometric progression?

  1. $1, 1, 1, 1, 1$
  2. $1, 2, 3, 4, 5$
  3. $2, 4, 6, 8, 10$
  4. $-1, 2, -3, 4, -5$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
Lets see option A:
Sequence is $1,1,1,1,1$
General form of GP is $a=1$ and $r=1$
Here ratio is constant throughout.
Thus in all options, option A is correct.
The geometric progression is $1,1,1,1,1,............$.

Multiple choice maths geometric sequences introduction to geometric progression understanding geometric progressions introduction to geometric progressions

The number of terms in a sequence $6, 12, 24, ....1536$ represents a

  1. arithmetic progression

  2. harmonic progression

  3. geometric progression

  4. geometric series
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation
Given series is $6,12,24,....1536$
Since, $\dfrac {12}{6} =2$ and $\dfrac {24}{12} =2$
i.e. the given sequence is a geometric sequence / progression. 
Multiple choice maths geometric sequences introduction to geometric progression understanding geometric progressions introduction to geometric progressions

Find out the general form of geometric progression.

  1. $2, 4, 8, 16$
  2. $2, -2, 2, 3, 1$
  3. $0, 3, 6, 9, 12$
  4. $10, 20, 30, 40$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The general form of geometric progression is $2, 4, 8, 16$.

Because here common ration between the consecutive terms is same. That is illustrated below.
$\dfrac {4}{2}=2, \dfrac {8}{4}=2, \dfrac {16}{8}=2$
Here the common ratio is $2$.

Multiple choice maths geometric sequences introduction to geometric progression understanding geometric progressions introduction to geometric progressions

For which sequence below can we use the formula for the general term of a geometric sequence?

  1. $1, 3, 5, 7, 9.....$
  2. $2, 4, 6, 8, 10.....$
  3. $4, 8, 16, 32, 64....$
  4. $1, -1, 3, -2, 4$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

For a G.P., the ratio must be common throughout.
We use the formula for the general term of a geometric sequence for $4, 8, 16, 32, 64.... $
Here the common ratio is $2$.

Multiple choice maths geometric sequences introduction to geometric progression understanding geometric progressions introduction to geometric progressions

An example of G.P. is

  1. $-1, \dfrac{1}{2}, \dfrac{1}{4}, \dfrac{1}{8}...$
  2. $ -1, \dfrac{3}{2}, \dfrac{1}{2}, -\dfrac{1}{2}$
  3. $1, \dfrac{1}{2}, \dfrac{1}{4}, \dfrac{1}{6}...$
  4. $1, \dfrac{1}{2}, \dfrac{1}{4}, \dfrac{1}{8}...$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

For a G.P., the ratio must be equal.
Here only D satisfies thiss condition.
So, an example of G.P. is $1, \dfrac{1}{2}, \dfrac{1}{4}, \dfrac{1}{8}...$
Here the common ratio is $\dfrac{1}{2}$.