Tag: understanding geometric progressions

Questions Related to understanding geometric progressions

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 $2$.

The series $a, ar, ar^2, ar^3, ar^4....$ is an

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

  1. finite geometric progression

  2. finite harmonic progression

  3. infinite geometric progression

  4. finite arithmetic progression

Show answer
Correct Option: C
Explanation:

$a, ar, ar^2, ar^3, ar^4....$ is an infinite geometric progression.

Here common ratio is $r$.
This can be found out as $\dfrac {ar}{a}=r, \dfrac {ar^2}{ar}=r$ and so on.
Thus the given series is in G.P.

The general form of GP $a, ar, ar^2, ar^3, ar^4$ is a

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

  1. finite geometric progression

  2. finite harmonic progression

  3. infinite geometric progression

  4. finite arithmetic progression

Show answer
Correct Option: A
Explanation:

Given sequence is $a,ar,ar^2, ar^3, ar^4$.

It is the general form of a finite geometric progression as the series stops at some point of finite terms.

$1 + 0.5 + 0.25 + 0.125....$ is an example of

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

  1. finite geometric progression

  2. infinite geometric series

  3. finite geometric sequence

  4. infinite geometric progression

Show answer
Correct Option: D
Explanation:

$1 + 0.5 + 0.25 + 0.125....$ is an example of infinite geometric progression.
Here the common ratio is $0.5$.
An infinite geometric series is the sum of an infinite geometric progression.

How will you identify the sequence is an infinite geometric progression?

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

  1. An geometric sequence containing finite number of terms

  2. An geometric sequence containing infinite number of terms

  3. An arithmetic sequence containing infinite number of terms

  4. An arithmetic sequence containing finite number of terms

Show answer
Correct Option: B
Explanation:

An geometric sequence containing infinite number of terms. It has a common ratio which is same throughout.
Example: $1 + 0.5 + 0.25 + 0.125....$ is an infinite geometric sequence.
Here the common ratio is $0.5$.