Sequences and Series Test

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Sequences and Series Test - 13

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Weekly Quiz Competition

Question 1
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 2
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 3
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 4
1 / -0

Find the next number in the series.
$$3, 6, 9, 12, 15,....$$

A
$$17$$

B
$$18$$

C
$$19$$

D
$$20$$

Solution

The next number is $$18$$.
Since the numbers are multiple of $$3$$.
$$3, 6, 9, 12, 15, \underline {18 }$$.
Question 5
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.
Question 6
1 / -0

Which of the following is $$GP?$$

A
$$2, 4, 8, 16$$

B
$$2, -2, 2, 3, 1$$

C
$$0, 3, 6, 9, 12$$

D
$$10, 20, 30, 40$$

Solution

The sequence $$2, 4, 8, 16$$ is $$GP$$
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 $$2$$.
Question 7
1 / -0

The difference of the squares of two consecutive even integers is divisible by which of the following integers?

A
$$3$$

B
$$4$$

C
$$6$$

D
$$7$$

Solution

Let the two consecutive even integers be $$2n$$ and $$(2n+2)$$. Then, $${(2n+2)}^{2}=(2n+2+2n)(2n+2-2n)$$
$$=2(4n+2)$$
$$=4(2n+1)$$, which is divisible by $$4$$.
Question 8
1 / -0

The 8th term of the sequence 1, 1, 2, 3, 5, 8 ............... is

A
25

B
24

C
23

D
21

Solution

Actually it is Fibonacci sequence, in which next term is always sum of two previous terms.
As $$2=1+1$$
$$3=1+2$$
$$5=2+3$$
$$8=3+5$$
Therefore, next (7th) term$$=5+8=13$$
Hence, 7th term$$=8+13=21$$
Option D is correct.
Question 9
1 / -0

The sum of two numbers is $$80$$. If the larger number exceeds four times the smaller by $$5$$, what is the smaller number?

A
$$5$$

B
$$15$$

C
$$20$$

D
$$25$$

Solution

Given, sum of two numbers is $$80$$.
Let the smaller number be $$x$$
Thus the larger will be $$80 - x$$.
Also given, larger number exceeds four times the smaller number by $$5$$.
Therefore, $$ 80 - x = 4x + 5$$
$$\Rightarrow 5x = 75$$
$$\Rightarrow x = 15$$
Thus the smaller number is $$15$$.
Question 10
1 / -0

$$\left( { 2 }^{ 2 }+{ 4 }^{ 2 }+{ 6 }^{ 2 }+.......+{ 20 }^{ 2 } \right) =$$?

A
$$770$$

B
$$1155$$

C
$$1540$$

D
$$385\times 385$$

Solution

$$\left( { 2 }^{ 2 }+{ 4 }^{ 2 }+{ 6 }^{ 2 }+.......+{ 20 }^{ 2 } \right) ={ \left( 1\times 2 \right) }^{ 2 }+{ \left( 2\times 2 \right) }^{ 2 }+{ \left( 2\times 3 \right) }^{ 2 }+......+{ \left( 2\times 10 \right) }^{ 2 }\quad $$
$$=\left( { 2 }^{ 2 }\times { 1 }^{ 2 } \right) +\left( { 2 }^{ 2 }\times { 2 }^{ 2 } \right) +\left( { 2 }^{ 2 }\times { 3 }^{ 2 } \right) +....+\left( { 2 }^{ 2 }\times { 10 }^{ 2 } \right) $$
$$=(4\times 5\times 77)$$
$$=1540$$

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Re-Attempt Weekly Quiz Competition

Sequences and Series Test - 13

Result

Sequences and Series Test - 13

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Question 1

110

115

120

125

Solution

Question 2

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

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

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

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

Solution

Question 3

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

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

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

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

Solution

Question 4

$$17$$

$$18$$

$$19$$

$$20$$

Solution

Question 5

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

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

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

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

Solution

Question 6

$$2, 4, 8, 16$$

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

$$0, 3, 6, 9, 12$$

$$10, 20, 30, 40$$

Solution

Question 7

$$3$$

$$4$$

$$6$$

$$7$$

Solution

Question 8

25

24

23

21

Solution

Question 9

$$5$$

$$15$$

$$20$$

$$25$$

Solution

Question 10

$$770$$

$$1155$$

$$1540$$

$$385\times 385$$

Solution

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