CBSE Class 10 Mathematics Arithmetic Progression Worksheet Set 12

MCQ

Question. Find \( 15^{\text{th}} \) terms of an AP \( 15, 10, 5, 0, -5, \dots \)
(a) -55
(b) -60
(c) -65
(d) None of the options
Answer: (a) -55

Question. If \( 18, a, b, -3 \) are in AP, then find \( a + b \)
(a) 15
(b) 10
(c) 25
(d) - 15
Answer: (a) 15

Question. If the \( n^{\text{th}} \) term of an AP is \( (2n + 1) \) then find the sum of its first three terms.
(a) 15
(b) 10
(c) 25
(d) - 15
Answer: (a) 15

Question. If the common difference of an A.P. is 3, then find \( a_{20} - a_{15} \)
(a) 15
(b) 13
(c) 25
(d) 35
Answer: (a) 15

Question. If \( 7^{\text{th}} \) term of an AP is 34 and \( 13^{\text{th}} \) term is 64 then \( 18^{\text{th}} \) term is
(a) 89
(b) 87
(c) 90
(d) 88
Answer: (a) 89

Question. The next term of an AP \( \sqrt{7}, \sqrt{28}, \sqrt{63}, \dots \)
(a) \( \sqrt{84} \)
(b) \( \sqrt{70} \)
(c) \( \sqrt{97} \)
(d) \( \sqrt{112} \)
Answer: (a) \( \sqrt{84} \)

Question. If an A.P. if \( a = 4, n = 7, d = 4 \) then \( a_n \) is
(a) 28
(b) 6
(c) 20
(d) 7
Answer: (a) 28

Question. What is common difference of an AP. in which \( a_{18} - a_{14} = 32 \)
(a) 8
(b) -8
(c) -4
(d) 4
Answer: (a) 8

Question. The sum of first 20 even natural number is
(a) 420
(b) 100
(c) 220
(d) 400
Answer: (a) 420

Question. In an A.P. if \( a = -7.2, d = 3.6, a_n = 7.2 \) then \( n \) is
(a) 5
(b) 3
(c) 1
(d) 4
Answer: (a) 5

Question. Write next terms of an AP \( \sqrt{2}, \sqrt{8}, \sqrt{18}, \sqrt{32}, \dots \)
(a) \( \sqrt{40} \)
(b) \( \sqrt{50} \)
(c) \( \sqrt{64} \)
(d) \( \sqrt{112} \)
Answer: (b) \( \sqrt{50} \)

Question. How many natural numbers are there between 200 and 500, which are divisible by 7?
(a) 42
(b) 43
(c) 63
(d) 53
Answer: (b) 43

Question. The common difference of an AP is 8. Find the difference of its \( 20^{\text{th}} \) and \( 15^{\text{th}} \) term
(a) 42
(b) 40
(c) 63
(d) 53
Answer: (b) 40

Question. The sum of first five multiple of 3 is
(a) 35
(b) 45
(c) 63
(d) 53
Answer: (b) 45

Question. The sum first \( n \) odd natural number is
(a) \( 2n-1 \)
(b) \( n^2 \)
(c) \( 2n+1 \)
(d) \( n^2 - 1 \)
Answer: (b) \( n^2 \)

Question. The \( 21^{\text{st}} \) term of an AP. whose first two terms are \( -3 \) and \( 4 \) is
(a) 17
(b) 143
(c) 137
(d) 153
Answer: (c) 137

Question. How many three- digit numbers are divisible by 7?
(a) 117
(b) 143
(c) 128
(d) 158
Answer: (c) 128

Question. The \( 4^{\text{th}} \) term from the end of an AP, \( -11, -8, -5, \dots, 49 \)
(a) 17
(b) 25
(c) 40
(d) - 40
Answer: (c) 40

Question. For the A.P. \( 3/2, 1/2, -1/2, -3/2 \) write common difference
(a) 1
(b) 14
(c) -1
(d) 3/2
Answer: (c) -1

Question. If \( 6/5, a, 4 \) are in AP then value of \( a \) is
(a) 13/3
(b) 13/6
(c) 13/5
(d) 13/7
Answer: (c) 13/5

Assertion Reasoning Questions Arithmetic Progression

Directions:
(a) If both Assertion and Reason are correct and Reason is the correct explanation of Assertion.
(b) If both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion.
(c) If Assertion is correct but Reason is incorrect.
(d) If Assertion is incorrect but Reason is correct.

Question. 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.
Answer: (a) If both Assertion and Reason are correct and Reason is the correct explanation of Assertion.

Question. Assertion : If \( S_n \) is the sum of the first \( n \) terms of an A.P., then its \( n^{\text{th}} \) term \( a_n \) is given by \( a_n = S_n - S_{n-1} \).
Reason : The \( 10^{\text{th}} \) term of the A.P. \( 5, 8, 11, 14, \dots \) is 35.
Answer: (c) If Assertion is correct but Reason is incorrect.

Question. Assertion : The sum of the series with the \( n^{\text{th}} \) term, \( t_n = (9 - 5n) \) 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 \( S_n = \frac{n}{2}[2a+(n-1)d] \)
Answer: (d) If Assertion is incorrect but Reason is correct.

Question. Assertion: Sum of \( n \) terms in an A.P. is given by the formula: \( S_n = \frac{n}{2} \times [2a+(n-1)d] \)
Reason: Sum of first 15 terms of \( 2+5+8+\dots \) is 345.
Answer: (a) If both Assertion and Reason are correct and Reason is the correct explanation of Assertion.

Question. Assertion: The constant difference between any two terms of an AP is commonly known as common difference
Reason: the common difference of \( 2, 4, 6, 8 \) this A.P. sequence is 2
Answer: (a) If both Assertion and Reason are correct and Reason is the correct explanation of Assertion.

Question. Assertion: If numbers \( a, b, c \) are in A.P then \( b-a = c-b \)
Reason: given three numbers are in AP, then the common difference will be same.
Answer: (a) If both Assertion and Reason are correct and Reason is the correct explanation of Assertion.

Question. Assertion: the value of \( n \), if \( a = 10, d = 5, a_n = 95 \).
Reason: the formula of general term \( a_n \) is \( a_n = a+(n-1)d \).
Answer: (a) If both Assertion and Reason are correct and Reason is the correct explanation of Assertion.

Question. Assertion: The \( 11^{\text{th}} \) term of an AP is \( 7, 9, 11, 13 \dots \) is 67
Reason: if \( S_n \) is the sum of first \( n \) terms of an AP then its \( n^{\text{th}} \) term \( a_n \) is given by \( a_n = S_n + S_{n-1} \)
Answer: (d) If Assertion is incorrect but Reason is correct.

Question. Assertion: arithmetic mean between 5 and 90 is 47.5
Reason: arithmetic mean between two given number \( a, b \) is \( (a+b)/2 \)
Answer: (a) If both Assertion and Reason are correct and Reason is the correct explanation of Assertion.

Question. Assertion: Sum of natural number from 1 to 100 is 5050
Reason: Sum of \( n \) natural number is \( n(n+1)/2 \)
Answer: (a) If both Assertion and Reason are correct and Reason is the correct explanation of Assertion.

SA TYPE questions

Question. Write first four terms of the AP when first term is -2 and common difference is 0
Answer: -2, -2, -2, -2

Question. How many two digit numbers are divisible by 3?
Answer: 30

Question. In a flower bed there are 23 rose plants in the first row 21 in the second 19 in the third and so on. There are 5 rose plants in the last row. How many rows are there in the flower bed?
Answer: \( n = 10 \)

Question. Subba Rao stared work in 1995 at an annual salary of Rs 5000 and received an increament of Rs 200 each year. In Which year did his income reach Rs. 7000.
Answer: \( 11^{\text{th}} \) years

Question. Which terms of an AP : \( 3, 8, 13, 18, \dots \) is 78
Answer: \( 16^{\text{th}} \) term

Question. If \( 9^{\text{th}} \) term of an AP is zero, prove that its \( 29^{\text{th}} \) term is double the \( 19^{\text{th}} \) term.
Answer: [Solution provided in question prompt as part of proof]

Question. If \( a_n = 9 - 5n \) find sum of \( 15^{\text{th}} \) terms of an AP
Answer: - 465

Question. The taxi fare after each km when the fare is Rs 15 for the first km and Rs 8 each additional km find fare after 4 km.
Answer: 39

Question. A man saves Rs. 10 on the first day of the month Rs 20 on the second day Rs. 30 on the third day and so on What will be saving in 30 days
Answer: Rs 4500

Question. Find the number of all two-digit natural numbers which are divisible by 6.
Answer: 15