Sequences and Series Test 11

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Sequences and Series Test 11

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Weekly Quiz Competition

Question 1
1 / -0

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

A
arithmetic series

B
geometric series

C
arithmetic sequence

D
geometric sequence

Solution

$$10, 20, 40, 80$$ 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 $$2$$.
Question 2
1 / -0

The geometric sequence is also called as

A
geometric progression

B
arithmetic sequence

C
arithmetic series

D
geometric series

Solution

The sequence is also called as progression.
So, the geometric sequence can be called as the geometric progression.
Question 3
1 / -0

A progression of the form $$a, ar, ar^2$$, ..... is a

A
geometric series

B
arithmetic series

C
arithmetic progression

D
geometric progression

Solution

A progression of the form $$a, ar, ar^2$$, ..... is a geometric progression.
Geometric Progression refers to a sequence in which successor term of each term is obtained by multiplying a constant term.
Question 4
1 / -0

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

A
arithmetic progression

B
arithmetic series

C
geometric progression

D
geometric series

Solution

Given sequence 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.
Question 5
1 / -0

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

A
arithmetic sequence

B
geometric sequence

C
geometric series

D
harmonic sequence

Solution

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.
Question 6
1 / -0

Identify the geometric progression.

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

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

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

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

Solution

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 $$3$$.
Question 7
1 / -0

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

A
geometric series

B
arithmetic progression

C
arithmetic series

D
geometric sequence

Solution

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 $$(D)$$
Question 8
1 / -0

The common ratio is used in _____ progression.

A
arithmetic

B
geometric

C
harmonic

D
series

Solution

The common ratio is used in geometric progression.
For example: $$2,4,8,16,....$$
Here the common ratio is $$2$$.
Question 9
1 / -0

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

A
geometric sequence

B
arithmetic progression

C
arithmetic series

D
geometric series

Solution

$$1, 3, 9, 27, 81$$ 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.
Question 10
1 / -0

Which one of the following is a geometric progression?

A
$$3, 5, 9, 11, 15$$

B
$$4, -4, 4, -4, 4$$

C
$$12, 24, 36, 48$$

D
$$6, 12, 24, 36$$

Solution

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

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Sequences and Series Test 11

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Sequences and Series Test 11

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SHARING IS CARING

Question 1

arithmetic series

geometric series

arithmetic sequence

geometric sequence

Solution

Question 2

geometric progression

arithmetic sequence

arithmetic series

geometric series

Solution

Question 3

geometric series

arithmetic series

arithmetic progression

geometric progression

Solution

Question 4

arithmetic progression

arithmetic series

geometric progression

geometric series

Solution

Question 5

arithmetic sequence

geometric sequence

geometric series

harmonic sequence

Solution

Question 6

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

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

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

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

Solution

Question 7

geometric series

arithmetic progression

arithmetic series

geometric sequence

Solution

Question 8

arithmetic

geometric

harmonic

series

Solution

Question 9

geometric sequence

arithmetic progression

arithmetic series

geometric series

Solution

Question 10

$$3, 5, 9, 11, 15$$

$$4, -4, 4, -4, 4$$

$$12, 24, 36, 48$$

$$6, 12, 24, 36$$

Solution

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