Tag: geometric sequences

Questions Related to geometric sequences

Which one of the following is a geometric progression?

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

  1. $3, 5, 9, 11, 15$

  2. $4, -4, 4, -4, 4$

  3. $12, 24, 36, 48$

  4. $6, 12, 24, 36$

Show answer
Correct Option: B
Explanation:

$4, -4, 4, -4, 4$ is a geometric progression.
Here the common ratio is $-1$.

Option B is correct.

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

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

  1. $2 + 6 + 18 + 54 +...$

  2. $3 + 12 + 48 + 192 +....$

  3. $1 + 4 + 7 + 10 +....$

  4. $1 + 3 + 9 + 27 +....$

Show answer
Correct Option: C
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.

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

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

  1. $1, 1, 1, 1, 1$

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

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

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

Show answer
Correct Option: A
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 $1,1,1,1,1,............$.

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

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

  1. arithmetic progression

  2. harmonic progression

  3. geometric progression

  4. geometric series

Show answer
Correct Option: C
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. 

Find out the general form of geometric progression.

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

  1. $2, 4, 8, 16$

  2. $2, -2, 2, 3, 1$

  3. $0, 3, 6, 9, 12$

  4. $10, 20, 30, 40$

Show answer
Correct Option: A
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 $2$.

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

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

  1. $1, 3, 5, 7, 9.....$

  2. $2, 4, 6, 8, 10.....$

  3. $4, 8, 16, 32, 64....$

  4. $1, -1, 3, -2, 4$

Show answer
Correct Option: C
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 $2$.

An example of G.P. is

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

  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. $1, \dfrac{1}{2}, \dfrac{1}{4}, \dfrac{1}{8}...$

Show answer
Correct Option: D
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 $\dfrac{1}{2}$.

The common ratio is used in _____ progression.

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

  1. arithmetic

  2. geometric

  3. harmonic

  4. series

Show answer
Correct Option: B
Explanation:

The common ratio is used in geometric progression.

For example: $2,4,8,16,....$
Here the common ratio is $2$.

Which of the following is a general form of geometric sequence?

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

  1. {$2, 4, 6, 8, 10$}

  2. {$-1, 2, 4, 8, -2$}

  3. {$2, -2, 2, -2, 2$}

  4. {$3, 13, 23, 33, 43$}

Show answer
Correct Option: C
Explanation:

{$2, -2, 2, -2, 2$} is a general form of geometric sequence.

For a G.P, the ratio must be equal throughout.
Here the common ratio is $-1$.

The common ratio is calculated in

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

  1. A.P.

  2. G.P.

  3. H.P.

  4. I.P.

Show answer
Correct Option: B
Explanation:

The common ratio is calculated in G.P.
For example: $2,4,8,16,....$

Here the common ratio is $2$.