Sequences and Series Test 12

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Sequences and Series Test 12

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Weekly Quiz Competition

Question 1
1 / -0

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

A
geometric series

B
arithmetic sequence

C
geometric progression

D
harmonic sequence

Solution

The sequence $$6, 12, 24, 48....$$ is a geometric progression as the ratio here is common.
The common ratio in the given series is $$2$$.
Question 2
1 / -0

Which one of the following is not a geometric progression?

A
$$1, 2, 4, 8, 16, 32$$

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

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

D
$$6, 12, 24, 48$$

Solution

For geometric progression, the ratio of the consecutive terms should be equal.
Here $$12, 24, 36, 48$$ is not a geometric progression. Here only the difference is common i.e. $$12$$.
Rest all options have same common ratio i.e., in option A, the ratio is $$2$$. In option B, the ratio is $$-1$$.
And in option D, the ratio is $$2$$.
Here the given sequence is an arithmetic progression.
Question 3
1 / -0

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:

A
geometric sequence

B
arithmetic sequence

C
geometric series

D
none of these

Solution

$$3,3^2,3^3,3^4,....(r=3)$$
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.
Question 4
1 / -0

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

A
$$1, 1, 1, 1, 1$$

B
$$1, 2, 3, 4, 5$$

C
$$2, 4, 6, 8, 10$$

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

Solution

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 $$1,1,1,1,1,............$$.
Question 5
1 / -0

Which of the following is a geometric sequence?

A
{$$2, 4, 6, 8, 10$$}

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

C
{$$2, -2, 2, -2, 2$$}

D
{$$3, 13, 23, 33, 43$$}

Solution

For a G.P., the ratio must be equal throughout
{$$2, -2, 2, -2, 2$$} is a geometric sequence because the common ratio is $$-1$$.
Question 6
1 / -0

An example of G.P. is

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

B
$$ -1, \dfrac{3}{2}, \dfrac{1}{2}, -\dfrac{1}{2}$$

C
$$1, \dfrac{1}{2}, \dfrac{1}{4}, \dfrac{1}{6}...$$

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

Solution

For a G.P., the ratio of consecutive terms must be equal.
Here only D satisfies this condition.
So, an example of G.P. is $$1, \dfrac{1}{2}, \dfrac{1}{4}, \dfrac{1}{8}...$$
Here the common ratio is $$\dfrac{1}{2}$$.
Question 7
1 / -0

Identify a geometric progression.

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

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

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

D
$$1, -1, 3, -2, 4$$

Solution

For a G.P., the ratio must be common throughout.
Thus the sequence $$4, 8, 16, 32, 64.... $$ is a geometric progression because the common ratio is $$2.$$
Question 8
1 / -0

The average IQ of $$4$$ people is $$110$$. If three of these people each have an IQ of $$105$$, what is the IQ of the fourth person?

A
110

B
115

C
120

D
125

Solution

Average IQ of $$4$$ people $$=110$$
$$\therefore$$ total IQ of $$4$$ people $$=$$ $$110\times 4=440$$
Average IQ of $$3$$ people $$=105$$
$$\therefore $$ total IQ of $$3$$ people $$=$$ $$105\times 3=315$$
Then IQ of forth person $$=$$ $$440-315=125$$
Question 9
1 / -0

A bag contains Rs. $$112$$ in the form of $$1$$-rupee, $$50$$-paise and $$10$$-paise coins in the ratio $$3 : 8 : 10$$. What is the number of $$50$$-paise coins?

A
$$112$$

B
$$128$$

C
$$96$$

D
$$24$$

Solution

Here bag contains Rs. $$112$$ in the form of $$1$$-rupee, $$50$$-paise and $$10$$-paise.
Coin ratio is $$ 3 : 8 : 10$$.
Value ratio $$= 3 \times 1: 8\times \dfrac {1}{2} : 10 \times \dfrac {1}{10}$$
$$= 3 : 4 : 1$$
Number of $$50$$ paise coins $$= \dfrac {4}{8} \times$$ Rs. $$112 =$$ Rs. $$56$$
Therefore, number of $$50$$ paise coins $$= 2\times 56 = 112$$.
Question 10
1 / -0

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

A
$$2, 6, 18, 54, ....$$

B
$$3, 12, 48, 192, ....$$

C
$$1, 4, 7, 10, ....$$

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

Solution

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.

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Sequences and Series Test 12

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Sequences and Series Test 12

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Question 1

geometric series

arithmetic sequence

geometric progression

harmonic sequence

Solution

Question 2

$$1, 2, 4, 8, 16, 32$$

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

$$12, 24, 36, 48$$

$$6, 12, 24, 48$$

Solution

Question 3

geometric sequence

arithmetic sequence

geometric series

none of these

Solution

Question 4

$$1, 1, 1, 1, 1$$

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

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

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

Solution

Question 5

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

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

{$$2, -2, 2, -2, 2$$}

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

Solution

Question 6

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

$$ -1, \dfrac{3}{2}, \dfrac{1}{2}, -\dfrac{1}{2}$$

$$1, \dfrac{1}{2}, \dfrac{1}{4}, \dfrac{1}{6}...$$

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

Solution

Question 7

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

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

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

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

Solution

Question 8

110

115

120

125

Solution

Question 9

$$112$$

$$128$$

$$96$$

$$24$$

Solution

Question 10

$$2, 6, 18, 54, ....$$

$$3, 12, 48, 192, ....$$

$$1, 4, 7, 10, ....$$

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

Solution

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