Assertion & Reason Test: Arithmetic Progressions - 2 - Class 10 MCQ

# Assertion & Reason Test: Arithmetic Progressions - 2 - Class 10 MCQ

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

### DIRECTION : In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as: Assertion : Three consecutive terms 2k +1, 3k+3and 5k -1 form an AP than k is equal to 6. Reason : In an AP a,a +d , a+2d, .........., the sum to n terms of the AP be  and d is constant.

Detailed Solution for Assertion & Reason Test: Arithmetic Progressions - 2 - Question 1

For 2k +1, 3k + 3 and 5k -1 to form an AP

(3k + 3) - (2k + 1) = (5k -1) - (3k + 3)

k + 2 = 2k - 4

2 + 4 = 2k - k = k

k = 6

In reason as given d = constan

So, both A and R are correct and R does explain A.

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

### DIRECTION : In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:Assertion : The sum of the first n terms of an AP is given by Sn = 3n2 -4 . Then n its nth term an = 6n -7 .Reason : n th term of an AP, whose sum to n terms is Sn , is given by an =Sn - Sn - 1

Detailed Solution for Assertion & Reason Test: Arithmetic Progressions - 2 - Question 2
n th term of an AP be an = Sn - Sn - 1

an = 3n2 - 4n- 3(n - 1)2 + 4)(n - 1)

an = 6n - 7

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

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Assertion & Reason Test: Arithmetic Progressions - 2 - Question 3

### 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 an AP in which a21 -a7 = 84 is 14.Reason : n th term of AP is given by an = a + (n - 1)d

Detailed Solution for Assertion & Reason Test: Arithmetic Progressions - 2 - Question 3
We have, an = a + (n - 1)d

a21 -a7 = {a + (21 - 1)d}

- {a + (7 - 1)d} = 84

a + 20d- a - 6d = 84

14d = 84

d = 18/14 = 6

d = 6

So, A is incorrect but R is correct

Assertion & Reason Test: Arithmetic Progressions - 2 - Question 4

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

Assertion : Arithmetic between 8 and 12 is 10.

Reason : Arithmetic between two numbers ‘a ’ and 'b' is given as

Detailed Solution for Assertion & Reason Test: Arithmetic Progressions - 2 - Question 4
Both are correct and Reason is the correct explanation for the Assertion.
Assertion & Reason Test: Arithmetic Progressions - 2 - Question 5

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

Assertion : Let the positive numbers a,b,c be in A.P., then 1/bc, 1/ac, 1/ab are also in A.P.

Reason : If each term of an A.P. is divided by abc, then the resulting sequence is also in A.P.

Detailed Solution for Assertion & Reason Test: Arithmetic Progressions - 2 - Question 5

if a,b,c are in AP, then b − a = c − b

a + c = 2b

For 1/bc, 1/ac, 1/ab ​

= 1/ac - 1/bc = b - a / abc

1/ac - 1/ac = c - a/abc

From above two equations,

1/bc, 1/ac, 1/ab ​ are also in AP.

And their common difference is divided by abc since numbers are also divided by abc.

So, if a,b,c are in AP and you divide the numbers by their product abc they will remain in AP.

Assertion & Reason Test: Arithmetic Progressions - 2 - Question 6

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

Assertion : Sum of first 10 terms of the arithmetic progression - 0.5 , - 1.0, - 1.5 , .......... is -27.5

Reason : Sum of n terms of an A.P. is given as where a = first term, d = common difference.

Detailed Solution for Assertion & Reason Test: Arithmetic Progressions - 2 - Question 6

Both are correct. Reason is the correct reasoning for Assertion.

Assertion,

= 5 [- 1 - 4.5]

= 5 (- 5.5) = -27.5

Assertion & Reason Test: Arithmetic Progressions - 2 - Question 7

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

Assertion : The sum of the series with the nth term. tn = (9 - 5n) is (465), when no. of terms n = 15 .

Reason : Given series is in A.P. and sum of n terms of an A.P. is

Detailed Solution for Assertion & Reason Test: Arithmetic Progressions - 2 - Question 7
Given: an = 9 – 5n

Taking n = 1,

a1 = 9 – 5(1) = 9 – 5 = 4

Taking n = 2,

a2 = 9 – 5(2) = 9 – 10 = -1

Taking n = 3,

a3 = 9 – 5(3) = 9 – 15 = -6

Therefore the series is 4, -1, -6, …

So, a = 4, d = a2 – a1 = -1 – 4 = -5

Now, we have to find the sum of the first 15 terms of the AP

⇒ S15 = 15 × (-31)

⇒ S15 = -465

Hence, the sum of 15 terms is -465.

Assertion & Reason Test: Arithmetic Progressions - 2 - Question 8

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

Assertion : If n th term of an A.P. is 7 -4n , then its common differences is -4.

Reason : Common difference of an A.P. is given by d =an + 1 - an

Detailed Solution for Assertion & Reason Test: Arithmetic Progressions - 2 - Question 8
Both are correct. Reason is the correct explanation.

Assertion, an = 7 - 4n

d = an + 1 -an

= 7 - 4 (n + 1) - 7 (-4n)

= 7 - 4n - 4 - 7 + 4n = - 4

Assertion & Reason Test: Arithmetic Progressions - 2 - 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 : If Sn is the sum of the first n terms of an A.P., then its nth term an is given by an =Sn - Sn - 1 .

Reason : The 10th term of the A.P. 5, 8, 11, 14, .......... is 35.

Detailed Solution for Assertion & Reason Test: Arithmetic Progressions - 2 - Question 9
Assertion (A) is true but reason (R) is false.

a10 = a + 9d

= 5 + 9(3) = 5 + 27 = 32

Assertion & Reason Test: Arithmetic Progressions - 2 - 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 : Sum of first hundred even natural numbers divisible by 5 is 500.

Reason : Sum of first n -terms of an A.P. is given by where ℓ = last term.

Detailed Solution for Assertion & Reason Test: Arithmetic Progressions - 2 - Question 10
Assertion : Even natural numbers divisible by 5 are 10, 20, 30, 40, ..........

They form an A.P. with,

a = 10 , d = 10

Reason is correct.

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