Sequences and Series Test

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Sequences and Series Test - 12

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Weekly Quiz Competition

Question 1
1 / -0

I thought of a decimal number. After I had multiplied it by 2, then added 1.5 and then divided by 3, I got 3.5. What was the decimal number?

A
7.1

B
5.6

C
5.8

D
4.5

Solution

Let the decimal number be $$x.$$
$$\dfrac{x\times 2+1.5}{3}=3.5$$
$$2x+1.5=3.5\times 3$$
$$2x+1.5=10.5$$
$$2x=9$$
$$x=\dfrac{9}{2}$$
$$x=4.5$$
Hence, correct option is D.
Question 2
1 / -0

If $$\displaystyle t_{3}=15,S_{10}=120$$ then the tenth term of the series i:

A
$$\displaystyle 6\frac{3}{5}$$

B
$$\displaystyle 5\frac{3}{5}$$

C
$$\displaystyle 6\frac{4}{5}$$

D
$$\displaystyle 6\frac{3}{4}$$

Solution

$$\displaystyle t_{3}=a+2d=15$$ ....(i)
$$\displaystyle S_{10}=\frac{10}{2}\left [ 2a+9d \right ]=120$$
$$\displaystyle S_{10}\Rightarrow 2a+9d=24$$ ....(ii)
(i) and (ii) gives $$\displaystyle a=\frac{87}{5}$$ and $$\displaystyle d=-\frac{6}{5}$$
$$\displaystyle \therefore t_{10}=a+9d=\frac{87}{5}+9\times \left ( -\frac{6}{5} \right )$$
$$\displaystyle =6\frac{3}{5}$$
Question 3
1 / -0

How many numbers are there between 500 and 600 in which 9 occurs only once?

A
19

B
18

C
10

D
9

Solution

509 , 519 , 529 , 539 , 549 , 559 , 569 , 579 , 589 , 590 , 591 , 592 ,

593 , 594 , 595 , 596 , 597 , 598 ...as 9 has to be occurred only once

so 599 would not be there so only 18 numbers are there.
Question 4
1 / -0

Answer the following set of questions by reading the above pitctograph. Number of TV sets sold in the year 2005 is

A
$$1000$$

B
$$500$$

C
$$50$$

D
$$2000$$

Solution

In the given pictogram the year 2005 depicts only one television figure.
When each television figure represents 500 TV sets, number of TV sets sold in the year 2005 is 500.
So, option B is the correct answer.
Question 5
1 / -0

If there are five consecutive integer in a series and the first integer is $$1$$, what is the value of the last consecutive integer?

A
$$2$$

B
$$3$$

C
$$4$$

D
$$5$$

Solution

Let the five consecutive integers be $$x, x + 1, x + 2, x + 3$$ and $$x + 4$$.
Therefore, the value of first integer is $$1$$ i.e., $$x = 1$$
So, the last integer is $$x + 4$$
The value of last integer $$= 5$$.
Question 6
1 / -0

Find a wrong number in the series: 7, 28, 63, 124, 215, 342, 511

A
7

B
28

C
124

D
215

E
342

Solution

Clearly , the correct sequence is:
$$\displaystyle 2^{3}-1$$, $$\displaystyle 3^{3}-1$$, $$\displaystyle 4^{3}-1$$, $$\displaystyle 5^{3}-1$$, $$\displaystyle 6^{3}-1$$, $$\displaystyle 7^{3}-1$$, $$\displaystyle 8^{3}-1$$.
$$ 3^{3}-1$$.
i.e. Hence, the answer is (b)
Question 7
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 8
1 / -0

$$10,$$ __$$, 15, 15, 20, 20, 25, 25,...$$. What number should fill the blank?

A
7

B
8

C
10

D
15

Solution

Here addition with repetition series, each number in the series repeats itself, and then increases by $$5$$ to get the next number.
The next number is $$10$$.
Question 9
1 / -0

$$2, 3, 6, n, 42, . . .$$
Find the value of $$n$$ in the above series.

A
$$9$$

B
$$12$$

C
$$15$$

D
$$18$$

E
$$21$$

Solution

Given series is $$2,3,6,n,42.....$$
we can decode the series, by multiplying the previous number by $$3$$ and then subtracting $$3$$ from it.
As we can see, $$2$$ being the first number of series
$$2\times 3=6$$
$$6-3=3$$ ( $$3$$ is second number)
$$3\times 3-3$$$$=6$$ ($$6$$ is $$3^{rd}$$ number)
$$n$$ will be $$6\times 3-3=18-3=15$$
$$n$$ is $$15$$
Question 10
1 / -0

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

A
arithmetic progression

B
arithmetic series

C
geometric series

D
geometric sequence

Solution

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

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Re-Attempt Weekly Quiz Competition

Sequences and Series Test - 12

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Sequences and Series Test - 12

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SHARING IS CARING

Question 1

7.1

5.6

5.8

4.5

Solution

Question 2

$$\displaystyle 6\frac{3}{5}$$

$$\displaystyle 5\frac{3}{5}$$

$$\displaystyle 6\frac{4}{5}$$

$$\displaystyle 6\frac{3}{4}$$

Solution

Question 3

19

18

10

9

Solution

Question 4

$$1000$$

$$500$$

$$50$$

$$2000$$

Solution

Question 5

$$2$$

$$3$$

$$4$$

$$5$$

Solution

Question 6

7

28

124

215

342

Solution

Question 7

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

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

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

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

Solution

Question 8

7

8

10

15

Solution

Question 9

$$9$$

$$12$$

$$15$$

$$18$$

$$21$$

Solution

Question 10

arithmetic progression

arithmetic series

geometric series

geometric sequence

Solution

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