Tag: maths

Questions Related to maths

$10,20,40,80$ is an example of

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

  1. fibonacci sequence

  2. harmonic sequence

  3. arithmetic sequence

  4. geometric sequence

Show answer
Correct Option: D
Explanation:

$10, 20, 40, 80$ is an example of geometric sequence.
In geometric sequence, the ratio of succeeding term to the preceeding term is always equal.

Here the common ratio is $2$.

$5 + 25 + 125 +.....$ is an example of 

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

  1. arithmetic progression

  2. arithmetic series

  3. geometric series

  4. geometric sequence

Show answer
Correct Option: C
Explanation:

In geometric series, the ratio should be equal.
Here $5 + 25 + 125 +....$ is an example of  geometric series as their common ratio is $5$.

A ______ is the sum of the numbers in a geometric progression.

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

  1. arithmetic progression

  2. arithmetic series

  3. geometric series

  4. geometric sequence

Show answer
Correct Option: C
Explanation:

A geometric series is the sum of the numbers in a geometric progression.

Identify the geometric series.

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

  1. $1 + 3 + 5 + 7 +....$

  2. $2 + 12 + 72 + 432...$

  3. $2 + 3 + 4 + 5 +...$

  4. $11 + 22 + 33 + 44+...$

Show answer
Correct Option: B
Explanation:

Geometric series is of the following form:

$a+ar+ar^2+ar^3 +ar^4+..........+ar^n$
Series $2+12+72+432+......$ follows the same with $a=2$ and $r=6$.
Hence, option B is correct.

The sequence $6, 12, 24, 48....$ is a

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

  1. geometric series

  2. arithmetic sequence

  3. geometric progression

  4. harmonic sequence

Show answer
Correct Option: C
Explanation:

The sequence $6, 12, 24, 48....$ is a geometric progression as the ratio here is common.
The common ratio in the given series is $2$.

$1, 3, 9, 27, 81$ is a

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

  1. geometric sequence

  2. arithmetic progression

  3. harmonic sequence

  4. geometric series

Show answer
Correct Option: A
Explanation:

$1, 3, 9, 27, 81$ is a geometric sequence.
A geometric progression is 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.

$4, \dfrac{8}{3}, \dfrac{16}{9}, \dfrac{32}{27}..$ is a

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

  1. arithmetic sequence

  2. geometric sequence

  3. geometric series

  4. harmonic sequence

Show answer
Correct Option: B
Explanation:

lets check the ratio between the consecutive terms.
$\dfrac {\frac {8}{3}}{4}=\dfrac {8}{12}=\dfrac {2}{3}$
Again take the ratio between next consecutive terms.
$\dfrac {\frac {16}{9}}{\frac {8}{3}}=\dfrac {16\times 3}{9\times 8}=\dfrac {2}{3}$
Here the common ratio is same $\dfrac{2}{3}$ throughout.
Hence, $4, \dfrac{8}{3}, \dfrac{16}{9}, \dfrac{32}{27}..$ is a geometric sequence.

In a _______ each term is found by multiplying the previous term by a constant.

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

  1. geometric sequence

  2. arithmetic sequence

  3. geometric series

  4. harmonic sequence

Show answer
Correct Option: A
Explanation:
Sol:
We know that if a,b,c are in G.p then $b^2=ac$
We know that a G.P
$a,ar,ar^2.ar^3-----ar^n$
${ a } _{ 1 }{ ,a } _{ 2 },{ a } _{ 3 },{ a } _{ 4 },----{ a } _{ n }$
$\dfrac { { a } _{ 2 } }{ { a } _{ 1 } } =\dfrac { { a } _{ 3 } }{ { a } _{ 2 } } =\dfrac { { a } _{ 3 } }{ { a } _{ 3 } } ----\dfrac { { a } _{ n } }{ { a } _{ n-1 } } =r$  (r=constant)
Therefore in a geometric progression each term is found multiplying the previous term by constant .

If a sequence of values follows a pattern of multiplying a fixed amount times each term to arrive at the following term, it is called a: 

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

  1. geometric sequence

  2. arithmetic sequence

  3. geometric series

  4. harmonic sequence

Show answer
Correct Option: A
Explanation:
$3,3^2,3^3,3^4,....(r=3)$
In a sequence if a fixed amount/constant is multiplied to each term to get the successive term the sequence is called geometric sequence.
Here $3$ is the constant which gets multiplied to each term to obtain the successive term.

Identify the geometric progression.

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. $5, 10, 15, 25, 35..$

  4. $1, 3, 9, 27, 81...$

Show answer
Correct Option: D
Explanation:

A geometric sequence is 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.
So, $1, 3, 9, 27, 81...$ is a geometric progression.
Here the common ratio is $3$.