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Assertion & Reason Test: Arithmetic Progressions - 1 - Class 10 MCQ


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10 Questions MCQ Test Mathematics (Maths) Class 10 - Assertion & Reason Test: Arithmetic Progressions - 1

Assertion & Reason Test: Arithmetic Progressions - 1 for Class 10 2024 is part of Mathematics (Maths) Class 10 preparation. The Assertion & Reason Test: Arithmetic Progressions - 1 questions and answers have been prepared according to the Class 10 exam syllabus.The Assertion & Reason Test: Arithmetic Progressions - 1 MCQs are made for Class 10 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Assertion & Reason Test: Arithmetic Progressions - 1 below.
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Assertion & Reason Test: Arithmetic Progressions - 1 - Question 1

Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.

Assertion (A): 184 is the 50th term of the sequence 3, 7, 11, …………

Reason (R): The nth term of A.P. is given by an = a + (n – 1)d

Detailed Solution for Assertion & Reason Test: Arithmetic Progressions - 1 - Question 1
let us check the position of 184 in the sequence,

an = a + (n – 1)d

184 = 3 +(n – 1)4

[a = 3 and d = 7– 3 = 4]

181 = (n – 1)4

45.25 = (n – 1)

The value of n can’t be negative.

Therefore, A is false but R is true

Assertion & Reason Test: Arithmetic Progressions - 1 - Question 2

Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.

Assertion (A): Common difference of the A.P: -5,-1, 3, 7,……. is 4.

Reason (R): Common difference of the A.P. a, a + d, a + 2d, …….., is given by d = 2nd term – 1st term.

Detailed Solution for Assertion & Reason Test: Arithmetic Progressions - 1 - Question 2
Common difference is the difference between two successive terms in A.P.

d = 2nd term – 1st term = – 1 – (– 5) = –1 + 5 = 4 Therefore, Both A and R are true and R is the correct explanation for A.

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Assertion & Reason Test: Arithmetic Progressions - 1 - Question 3

Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.

Assertion (A): Sum of first hundred even natural numbers divisible by 5 is 500.

Reason (R): Sum of first n terms of an A.P is given l is last term

Detailed Solution for Assertion & Reason Test: Arithmetic Progressions - 1 - Question 3
First hundred even natural numbers divisible by 5 are

10, 20, 30, 40, 50............1000

If last term is 1000, then sum of all these numbers can’t be 500

Therefore, A is false but R is true.

Assertion & Reason Test: Arithmetic Progressions - 1 - Question 4

Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.

Assertion (A): Sum of all 11 terms of an A.P whose middle most term is 30 is 330.

Reason (R): Sum of first n terms of an A.P is given by l is the middle term

Detailed Solution for Assertion & Reason Test: Arithmetic Progressions - 1 - Question 4
Middle most term =

a6 = a + 5d = 30

= 11 × 30 = 330

Also, Sum of first n terms of an A.P is given by is last term(Here we can’t apply this formula as no last term is mentioned in the statement.)

Therefore, A is true but R is false.

Assertion & Reason Test: Arithmetic Progressions - 1 - Question 5

Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.

Assertion (A): If the nth term of an A.P. is 7 – 4n, then its common differences is – 4.

Reason (R): Common differences of an A.P. is given by d = an + 1 – an

Detailed Solution for Assertion & Reason Test: Arithmetic Progressions - 1 - Question 5
We are given, an = 7 – 4n

Also, an + 1 = 7 – 4(n + 1) = 7 – 4n – 4 = 3 – 4n

d = a(n + 1)–an

= 3 – 4n – 7 + 4n = – 4

Therefore, Both A and R are true and R is the correct explanation for A.

Assertion & Reason Test: Arithmetic Progressions - 1 - Question 6

Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.

Assertion (A): If five times the fifth term of an A.P. is equal to eight times its eighth term, then its 13th term is zero.

Reason (R): Common difference of the A.P. a, a + d, a + 2d, …….., is given by d = 2nd term – 1st term.

Detailed Solution for Assertion & Reason Test: Arithmetic Progressions - 1 - Question 6
Let the first term and common difference of the A.P. are a and d

5(a + 4d) = 8(a + 7d)

5a + 20d = 8a + 56d

3a + 36d = 0

a + 12d = 0

So, a13 = 0, which is true

Also, the expression d = 2nd term – 1st term

Therefore, Both A and R are true and R is not correct explanation for A.

Assertion & Reason Test: Arithmetic Progressions - 1 - Question 7

Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.

Assertion (A): There will be 10 rows in the flower bed if there are 23 plants in the first row, 21 in the second row, 19 in the third and so on. Also 5 rose plants are in the last row.

Reason (R): Sum of first n terms of an A.P is given by

Detailed Solution for Assertion & Reason Test: Arithmetic Progressions - 1 - Question 7
In case Assertion: According to given statement, Number of rows = 10 Number plants in rows, can be expressed in A.P.

i.e., 23, 21, 19, .........

a = 23

d = 21 – 23 = – 2

an = a + (n – 1)d

a10 = 23 + (10 – 1) (– 2)

a10 = 23 – 18

a10 = 5

∴ a10 = 5 = last row

So, Assertion (A) is correct.

As we are not given any information how many total plants are there so we can’t apply

Therefore, Both A and R are true and R is not correct explanation for A.

Assertion & Reason Test: Arithmetic Progressions - 1 - Question 8

Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.

Assertion (A): The sum of first n terms of an A.P is given by Sn = 3n2 – 4n. Then its n term is given by the term an = 6n – 7.

Reason (R): nth term of an A.P, whose sum to n terms is Sn, is given by an = Sn – Sn – 1

Detailed Solution for Assertion & Reason Test: Arithmetic Progressions - 1 - Question 8
To verify the reason, we are given Sn = 3n2 – 4n

Then, an – 1 = 3(n – 1)2 – 4(n – 1)

= 3n2 + 3 – 6n – 4n + 4 = 3n2 – 10n + 7

an = Sn – Sn – 1

an = 3n2 – 4n – (3n2 – 10n + 7) = 6n – 7

Reason is correct.

Therefore, Both A and R are true and R is the correct explanation for A.

Assertion & Reason Test: Arithmetic Progressions - 1 - Question 9

DIRECTION : In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:

Assertion : Common difference of the AP -5, -1, 3, 7, .......... is 4.

Reason : Common difference of the AP a,ad +a , d+ 2 , .......... is given by d = 2 nd term-1st term.

Detailed Solution for Assertion & Reason Test: Arithmetic Progressions - 1 - Question 9
Common difference, d = - 1-1(- 5) = 4

So, both A and R are correct and R explains A.

Assertion & Reason Test: Arithmetic Progressions - 1 - Question 10

DIRECTION : In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:

Assertion : an - an - 1 is not independent of n then the given sequence is an AP.

Reason : Common difference d =an - an - 1 is constant or independent of n .

Detailed Solution for Assertion & Reason Test: Arithmetic Progressions - 1 - Question 10
We have, common difference of an AP

d =an - an - 1 is independent of n or constant.

So, A is correct but R is incorrect.

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