PRACTICE SHEET
Subject: Mathematics Standard: X Division:
Chapter: 5
Name: Arithmetic Progression Roll No:
Section A: Multiple Choice Questions
Q1. If p, q, r and s are in AP then (r – q) is equal to
(a) s − p (b) s − q (c) s − r (d) p − s
Q2. Which of the following sequence is an AP?
(a) 2, 4, 8, 16, … (b) 3, 3 + √2 , 3 + 2√2 (c) 1, 3, 9, 27,.. (d) √3, √6, √9
Q3. The common difference of the AP:
√2, 2√2, 3√2, 4√2, … is
(a) 1 (b) √2 (c) 2√2 (d) −√2
Q4. If the first three terms of an AP are b, c, and 2b, then the ratio of b and c is
(a) 2:1 (b) 1:2 (c) 3:2 (d) 2:3
Q5. In an AP, if a = 28, d = −4, n = 7, then an is:
(a) 4 (b) 5 (c) 3 (d) 7
Q6. Two APs have the same common difference. If the first term of one of these is −1 and that of
the other is −8. Then the difference between their 4th terms is
(a) −1 (b) −8 (c) 7 (d) −9
Q7. If the first term of an AP is p and the common difference is q, then its 10th term is
(a) q + 9p (b) p − 9q (c) p + 9q (d) 2p + 9q
Q8. If the nth term of an AP is 7 – 4n, its common difference is
(a) −3 (b) 3 (c) −4 (d) 4
Q9. If the first term of an AP is 2 and common difference is 4, then sum of its first 40 terms is
(a) 3200 (b) 1600 (c) 3800 (d) 3600
Q10. In an AP, if the common difference is −4, and the seventh term is 4, then the first term is
(a) −20 (b) 28 (c) 20 (d) 16
Q11. How many three digit numbers are divisible by 7?
(a) 126 (b) 127 (c) 128 (d) 129
Q12. The sum of all positive even integers between 1 and 70 is
(a) 836 (b) 1024 (c) 1260 (d) 1190
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, PRACTICE SHEET
Q13. If the sum of the n terms of an AP is 3n2 + 5n, then which of its term is 164?
(a) 24th (b) 25th (c) 26th (d) 27th
Q14. If the sum of n terms of an AP is 3n2 − n and its common difference is 6, then its first term is
(a) 1 (b) 2 (c) 3 (d) 4
Q15. The sum of first 20 odd natural numbers is
(a) 210 (b) 300 (c) 400 (d) 420
Direction for questions 16 to 19: In question numbers 16 to 19, a statement of Assertion (A)
is followed by a statement of Reason (R). Choose the correct option.
Q16. Assertion (A): The 10th term of the AP 5, 8, 11, 14, ……… is 35.
Reason (R): If Sn is the sum of the first n terms of an AP, then its nth term is given by
an = Sn – Sn – 1.
(a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of
Assertion (A).
(b) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation
of Assertion (A).
(c) Assertion (A) is true but Reason (R) is false.
(d) Assertion (A) is false but Reason (R) is true.
Q17. Assertion (A): 199 is the 50th term of the sequence 3, 7, 11,…
Reason (R): The nth term of an AP is given by an = a + (n – 1)d
(a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of
Assertion (A).
(b) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation
of Assertion (A).
(c) Assertion (A) is true but Reason (R) is false.
(d) Assertion (A) is false but Reason (R) is true.
5 5
Q18. Assertion (A): −5, , 0, ,… is an Arithmetic Progression.
2 2
Reason (R): The terms of an Arithmetic Progression cannot have both positive and negative
rational numbers.
(a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of
Assertion (A).
(b) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation
of Assertion (A).
(c) Assertion (A) is true but Reason (R) is false.
(d) Assertion (A) is false but Reason (R) is true.
CB/X/2526 Practice Sheet Page 2 of 8
Subject: Mathematics Standard: X Division:
Chapter: 5
Name: Arithmetic Progression Roll No:
Section A: Multiple Choice Questions
Q1. If p, q, r and s are in AP then (r – q) is equal to
(a) s − p (b) s − q (c) s − r (d) p − s
Q2. Which of the following sequence is an AP?
(a) 2, 4, 8, 16, … (b) 3, 3 + √2 , 3 + 2√2 (c) 1, 3, 9, 27,.. (d) √3, √6, √9
Q3. The common difference of the AP:
√2, 2√2, 3√2, 4√2, … is
(a) 1 (b) √2 (c) 2√2 (d) −√2
Q4. If the first three terms of an AP are b, c, and 2b, then the ratio of b and c is
(a) 2:1 (b) 1:2 (c) 3:2 (d) 2:3
Q5. In an AP, if a = 28, d = −4, n = 7, then an is:
(a) 4 (b) 5 (c) 3 (d) 7
Q6. Two APs have the same common difference. If the first term of one of these is −1 and that of
the other is −8. Then the difference between their 4th terms is
(a) −1 (b) −8 (c) 7 (d) −9
Q7. If the first term of an AP is p and the common difference is q, then its 10th term is
(a) q + 9p (b) p − 9q (c) p + 9q (d) 2p + 9q
Q8. If the nth term of an AP is 7 – 4n, its common difference is
(a) −3 (b) 3 (c) −4 (d) 4
Q9. If the first term of an AP is 2 and common difference is 4, then sum of its first 40 terms is
(a) 3200 (b) 1600 (c) 3800 (d) 3600
Q10. In an AP, if the common difference is −4, and the seventh term is 4, then the first term is
(a) −20 (b) 28 (c) 20 (d) 16
Q11. How many three digit numbers are divisible by 7?
(a) 126 (b) 127 (c) 128 (d) 129
Q12. The sum of all positive even integers between 1 and 70 is
(a) 836 (b) 1024 (c) 1260 (d) 1190
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, PRACTICE SHEET
Q13. If the sum of the n terms of an AP is 3n2 + 5n, then which of its term is 164?
(a) 24th (b) 25th (c) 26th (d) 27th
Q14. If the sum of n terms of an AP is 3n2 − n and its common difference is 6, then its first term is
(a) 1 (b) 2 (c) 3 (d) 4
Q15. The sum of first 20 odd natural numbers is
(a) 210 (b) 300 (c) 400 (d) 420
Direction for questions 16 to 19: In question numbers 16 to 19, a statement of Assertion (A)
is followed by a statement of Reason (R). Choose the correct option.
Q16. Assertion (A): The 10th term of the AP 5, 8, 11, 14, ……… is 35.
Reason (R): If Sn is the sum of the first n terms of an AP, then its nth term is given by
an = Sn – Sn – 1.
(a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of
Assertion (A).
(b) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation
of Assertion (A).
(c) Assertion (A) is true but Reason (R) is false.
(d) Assertion (A) is false but Reason (R) is true.
Q17. Assertion (A): 199 is the 50th term of the sequence 3, 7, 11,…
Reason (R): The nth term of an AP is given by an = a + (n – 1)d
(a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of
Assertion (A).
(b) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation
of Assertion (A).
(c) Assertion (A) is true but Reason (R) is false.
(d) Assertion (A) is false but Reason (R) is true.
5 5
Q18. Assertion (A): −5, , 0, ,… is an Arithmetic Progression.
2 2
Reason (R): The terms of an Arithmetic Progression cannot have both positive and negative
rational numbers.
(a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of
Assertion (A).
(b) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation
of Assertion (A).
(c) Assertion (A) is true but Reason (R) is false.
(d) Assertion (A) is false but Reason (R) is true.
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