Sequences and Series Test 23

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Sequences and Series Test 23

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Weekly Quiz Competition

Question 1
1 / -0

Choose the missing number in the series: $$2, 2, 3, 4, 4,$$__$$, 6, 6, 7, 8, 8, 9....$$

A
5

B
6

C
7

D
8

Solution

This is a continuous series of adding $$1$$ to the previous number, in which every third number is not repeated.
So, the missing number is $$5$$.
Question 2
1 / -0

Find the value of $$'x'$$ in the series: $$144, 169, x, 225, 256, 289$$.

A
190

B
192

C
196

D
195

Solution

The series is a perfect square in increasing order of $$12, 13, 14, 15...$$
So, the value of $$x$$ is $$196$$.
Question 3
1 / -0

Find the missing number in the pattern: $$2, 5, 8, 11,$$ __$$, 17, 20, 23, 26$$

A
11

B
12

C
13

D
14

Solution

The series adds $$3$$ to each number to get the next number.
So, the next number is $$11 + 3 = 14$$
Question 4
1 / -0

Which pair of numbers comes next?
$$25, 23, 5, 20, 16, 5,....$$

A
$$11, 5$$

B
$$5, 6$$

C
$$10, 5$$

D
$$9, 5$$

Solution

This is an alternating subtraction series with the interpolation of a random number, $$5$$, as every third number.
In the subtraction series, $$2$$ is subtracted, then $$3$$ then $$4$$, and so on.
The next pair of numbers are $$11$$ and $$5$$.
Question 5
1 / -0

Which number comes next?
$$5, 9, 13, 17, 21, 25, 29,...$$

A
$$31$$

B
$$32$$

C
$$30$$

D
$$33$$

Solution

The series adds $$4$$ to each number to get the next number.
So, the next number is $$29 + 4 = 33$$
Question 6
1 / -0

$$2, 3,$$ __$$, 4, 4, 5, 6, 6, 6, 7, 7, 7...$$ What number should fill the blank?

A
$$1$$

B
$$2$$

C
$$3$$

D
$$4$$

Solution
Question 7
1 / -0

Which pair of numbers comes next?
$$10, 18, 12, 21, 15 ,25, ,....$$

A
$$19, 30$$

B
$$19, 27$$

C
$$30, 19$$

D
$$27, 19$$

Solution

This is an alternating addition series
First series = $$10, 10+2=12, 12+3=15$$. $$\therefore$$ next number= $$15+4=19$$
Second series = $$18, 18+3=21, 21+4=25$$ $$\therefore$$ next number = $$25+5=30$$
The next pair of numbers are $$19, 30$$.
Question 8
1 / -0

Fill in the blank: $$62, 66, 63, 66, 64,$$ __$$, 65,....$$

A
60

B
61

C
62

D
63

Solution

The series alternates the addition of $$4$$ with the subtraction of $$3$$.
So, the missing number is $$61$$.
Question 9
1 / -0

Identify the missing integer: $$9, 45,$$ ____$$, 1125, 5625...$$

A
$$220$$

B
$$223$$

C
$$224$$

D
$$225$$

Solution

This is continuous series multiplied by $$5$$.
$$9 \times 5 = 45$$
$$45 \times 5 = 225$$
$$225 \times 5 = 1,125$$
$$1,125 \times 5= 5,625.$$
So, the missing integer is $$225$$.
Question 10
1 / -0

The area of the triangle formed from points $$(1, 2), (2, 4)$$ and $$(3, 1)$$ is ____ square units.

A
$$\dfrac{5}{2}$$

B
$$\dfrac{2}{5}$$

C
$$\dfrac{3}{2}$$

D
$$2$$

Solution

Formula for area of triangle is $$\left|\dfrac{1}{2}[x_{1}(y_{2}-y_{3}) + x_{2} (y_{3} - y_{1}) + x_{3} (y_{1} - y_{2})] \right|$$
where $$x_{1} = 1$$, $$y_{1} = 2$$, $$x_{2} = 2$$, $$y_{2} = 4$$, $$x_{3} = 3$$ and $$y_{3} = 1$$
Substitute the values, we get,
Area of triangle $$=$$ $$\left|\dfrac{1}{2}\times[1(4 - 1) + 2(1 - 2) + 3(2 - 4)]\right|$$
$$=$$ $$\left|\dfrac{1}{2}\times[3 - 2 - 6]\right|$$
$$=$$ $$\left|\dfrac{1}{2}\times -5\right|$$
$$=$$ $$\left|-\frac{5}{2} \right|$$
Area always in absolute value.
So, area of the triangle $$= \dfrac{5}{2}$$ square units.

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Sequences and Series Test 23

Result

Sequences and Series Test 23

Score

-

Rank

-

SHARING IS CARING

Question 1

5

6

7

8

Solution

Question 2

190

192

196

195

Solution

Question 3

11

12

13

14

Solution

Question 4

$$11, 5$$

$$5, 6$$

$$10, 5$$

$$9, 5$$

Solution

Question 5

$$31$$

$$32$$

$$30$$

$$33$$

Solution

Question 6

$$1$$

$$2$$

$$3$$

$$4$$

Solution

Question 7

$$19, 30$$

$$19, 27$$

$$30, 19$$

$$27, 19$$

Solution

Question 8

60

61

62

63

Solution

Question 9

$$220$$

$$223$$

$$224$$

$$225$$

Solution

Question 10

$$\dfrac{5}{2}$$

$$\dfrac{2}{5}$$

$$\dfrac{3}{2}$$

$$2$$

Solution

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