Arithmetic Progressions Test

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Arithmetic Progressions Test - 28

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Weekly Quiz Competition

Question 1
1 / -0

3, 5, 7, 9, 11, 13, 15.... is an

A
Geometric progression

B
Harmonic progression

C
Arithmetic progression

D
None of above

Solution

3, 5, 7, 9, 11, 13, 15.... is an arithmetic progression.
Here the common difference between two consecutive terms is 2.
A sequence in which the difference between any two consecutive terms is a constant is called as arithmetic progression.
Question 2
1 / -0

A sequence of numbers in which each term is related to its predecessor by same law is called

A
arithmetic series

B
progression

C
geometric series

D
none of these

Solution

A sequence of numbers in which each term is related to its predecessor by same law is called progression
Example: 1, 2, 3, 4.... is an example of sequence or progression.
Since the given sequence follows a same rule or law through out the sequence and there is a relation between each term and it's previous one.
Question 3
1 / -0

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

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

B
$$0, 3, 6, 9, 12...$$

C
$$4, 5, 7, 10, 14...$$

D
$$-1, 2, 5, 8, 11..$$

Solution

For any series to be in Arithmetic Progression, the common difference (i.e., the difference between any two consecutive terms should be the same).
$$4, 5, 7, 10, 14...$$ is not in the form of A.P.
Here the common difference is not constant.
Question 4
1 / -0

________ can be defined as arrangement of terms in which sequence of terms follow some conditions.

A
Series

B
Preceding sequence

C
Progression

D
Geometric progression

Solution

Progression can be defined as arrangement of terms in which sequence of terms follow some conditions.
Question 5
1 / -0

_______ is a series of successive events.

A
Series

B
Preceding sequence

C
Progression

D
Geometric progression

Solution

Progression is a series of successive events.
Question 6
1 / -0

Which of the following is in the form of $$A.P$$?

A
$$1, -1, -3, -5, -7,\dots$$

B
$$0, 3, 2, 1, -2,\dots$$

C
$$4, 5, 7, 10, 14,\dots$$

D
$$-2, 2, -2, 2, -2,\dots$$

Solution

$$1, -1, -3, -5, -7$$ is in the form of $$A.P$$ because the common difference between consecutive terms of this sequence is constant and that is equal to $$-2$$.
Question 7
1 / -0

For given A.P. $$-\dfrac{1}{2}, -\dfrac{3}{2}, \dfrac{1}{2}, -\dfrac{3}{2}, ..$$ find the common difference.

A
$$-1$$

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

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

D
$$1$$

Solution

The general form of A.P. is $$a, a + d, a + 2d, a + 3d.....$$
$$-\dfrac{1}{2}, -\dfrac{3}{2}, \dfrac{1}{2}, -\dfrac{3}{2}, ..$$
Here the common difference is $$-1$$.
Question 8
1 / -0

Find the $$11$$th term of the sequence $$5,2,-1,-4,......$$

A
$$-25$$

B
$$-28$$

C
$$-22$$

D
None

Solution

$$ a_{1} = 5;d = a_{2}-a_{1} = 2-5 = -3 $$
$$ \therefore a_{11} = a+(n-1)d = 5+10(-3) $$
$$ \Rightarrow {a_{11} = -25} $$
Question 9
1 / -0

The nth term of the sequence $$2, 4, 6, 8....$$ is

A
$$n$$

B
$$n - 1$$

C
$$2n$$

D
$$2n - 4$$

Solution

Clearly, the difference of successive terms of above sequence is constant which is 2
So given sequence is in AP with first term 2 and common difference $$2$$
Hence general term is, $$a_n = a+(n-1)d=2+(n-1)2=2n$$
Hence option 'C' is correct choice
Question 10
1 / -0

Find the sum of all the odd positive integers less than $$100$$.

A
$$2400$$

B
$$2500$$

C
$$2525$$

D
$$2600$$

E
$$2650$$

Solution

The possible odd positive integers: $$1,3,5,7,9,11..........99$$
The first term, $$a$$ $$=1$$
The difference between two consecutive terms $$=3-1=2$$
The total no. of terms $$=50$$
Applying sum of arithmetic progression formula,
$$S_n=\dfrac{n}{2}[2a+(n-1)d]$$
$$=\dfrac{50}{2}[2\times1+(50-1)2]$$
$$=25(2+98)=2500$$
Hence, choice B is correct.

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Arithmetic Progressions Test - 28

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Arithmetic Progressions Test - 28

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SHARING IS CARING

Question 1

Geometric progression

Harmonic progression

Arithmetic progression

None of above

Solution

Question 2

arithmetic series

progression

geometric series

none of these

Solution

Question 3

$$1, -1, -3, -5, -7...$$

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

$$4, 5, 7, 10, 14...$$

$$-1, 2, 5, 8, 11..$$

Solution

Question 4

Series

Preceding sequence

Progression

Geometric progression

Solution

Question 5

Series

Preceding sequence

Progression

Geometric progression

Solution

Question 6

$$1, -1, -3, -5, -7,\dots$$

$$0, 3, 2, 1, -2,\dots$$

$$4, 5, 7, 10, 14,\dots$$

$$-2, 2, -2, 2, -2,\dots$$

Solution

Question 7

$$-1$$

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

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

$$1$$

Solution

Question 8

$$-25$$

$$-28$$

$$-22$$

None

Solution

Question 9

$$n$$

$$n - 1$$

$$2n$$

$$2n - 4$$

Solution

Question 10

$$2400$$

$$2500$$

$$2525$$

$$2600$$

$$2650$$

Solution

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