Tag: introduction to geometric progressions

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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 $\dfrac{1}{2}$.

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

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

  1. {$2, 4, 6, 8, 10$}
  2. {$-1, 2, 4, 8, -2$}
  3. {$2, -2, 2, -2, 2$}
  4. {$3, 13, 23, 33, 43$}
Reveal answer Fill a bubble to check yourself
C Correct answer
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 $-1$.

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

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

  1. finite geometric progression

  2. finite harmonic progression

  3. infinite geometric progression

  4. finite arithmetic progression
Reveal answer Fill a bubble to check yourself
C Correct answer
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.

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

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

  1. finite geometric progression

  2. finite harmonic progression

  3. infinite geometric progression

  4. finite arithmetic progression
Reveal answer Fill a bubble to check yourself
A Correct answer
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.

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

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

  1. finite geometric progression

  2. infinite geometric series

  3. finite geometric sequence

  4. infinite geometric progression
Reveal answer Fill a bubble to check yourself
D Correct answer
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.

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

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

  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
Reveal answer Fill a bubble to check yourself
B Correct answer
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 $0.5$.