Vardaan Learning Institute

Chapter Practice Sheet: Arithmetic Progressions

Class: 10 (CBSE) Subject: Mathematics Max. Marks: 50
SECTION A: OBJECTIVE TYPE QUESTIONS (1 Mark Each)
1. The nth term of the AP: 5, 2, -1, -4, ... is:
  1. 2n - 5
  2. 2n + 5
  3. 8 - 3n
  4. 3n - 8
[1]
2. If the common difference of an AP is 3, then $a_{20} - a_{15}$ is:
  1. 5
  2. 3
  3. 15
  4. 20
[1]
3. The first four terms of an AP whose first term is -2 and the common difference is -2 are:
  1. -2, 0, 2, 4
  2. -2, -4, -8, -16
  3. -2, -4, -6, -8
  4. -2, -2, -2, -2
[1]
4. The sum of the first five multiples of 3 is:
  1. 45
  2. 55
  3. 65
  4. 75
[1]
5. If k, 2k-1 and 2k+1 are three consecutive terms of an AP, the value of k is:
  1. 2
  2. -2
  3. 3
  4. -3
[1]
6. The 10th term from the end of the AP: 4, 9, 14, ..., 254 is:
  1. 209
  2. 205
  3. 214
  4. 213
[1]
7. The 11th term of the AP: -5, -5/2, 0, 5/2, ... is:
  1. -20
  2. 20
  3. -30
  4. 30
[1]
8. In an AP, if $d = -4, n = 7, a_n = 4$, then a is:
  1. 6
  2. 7
  3. 20
  4. 28
[1]
9. The sum of first n positive integers is given by:
  1. $n(n-1)/2$
  2. $n(n+1)/2$
  3. $n(n+1)$
  4. $n^2$
[1]
10. Assertion (A): The list of numbers 2, 4, 8, 16... is an AP.
Reason (R): The common difference is not constant.
  1. Both A and R are true and R is the correct explanation of A.
  2. Both A and R are true but R is not the correct explanation of A.
  3. A is true but R is false.
  4. A is false but R is true.
[1]
SECTION B: SHORT ANSWER TYPE QUESTIONS (2 Marks Each)
11. Find the sum of the first 22 terms of the AP: 8, 3, -2, ...
[2]
12. Which term of the AP: 3, 15, 27, 39, ... will be 132 more than its 54th term?
[2]
13. Find the number of terms in the AP: 7, 13, 19, ..., 205.
[2]
14. If the sum of the first n terms of an AP is $4n - n^2$, what is the 10th term?
[2]
SECTION C: SHORT ANSWER TYPE II QUESTIONS (3 Marks Each)
15. The sum of the 4th and 8th terms of an AP is 24 and the sum of the 6th and 10th terms is 44. Find the first three terms of the AP.
[3]
16. How many two-digit numbers are divisible by 3?
[3]
17. Find the sum of all odd integers between 2 and 100 which are divisible by 3.
[3]
18. If m times the mth term of an AP is equal to n times its nth term and $m \ne n$, show that the $(m+n)$th term of the AP is zero.
[3]
19. Which term of the AP: 121, 117, 113, ... is its first negative term?
[3]
20. If the sum of first 7 terms of an AP is 49 and that of 17 terms is 289, find the sum of first n terms.
[3]
SECTION D: LONG ANSWER TYPE QUESTIONS (5 Marks Each)
21. A spiral is made up of successive semicircles, with centres alternately at A and B, starting with centre at A, of radii 0.5 cm, 1.0 cm, 1.5 cm, 2.0 cm, ... as shown in Fig. What is the total length of such a spiral made up of 13 consecutive semicircles? (Take $\pi = 22/7$)
[5]
22. In a potato race, a bucket is placed at the starting point, which is 5 m from the first potato, and the other potatoes are placed 3 m apart in a straight line. There are 10 potatoes in the line. A competitor starts from the bucket, picks up the nearest potato, runs back with it, drops it in the bucket, runs back to pick up the next potato, runs to the bucket to drop it in, and she continues in the same way until all the potatoes are in the bucket. What is the total distance the competitor has to run?
[5]
SECTION E: CASE STUDY (4 Marks)
23. Case Study: Savings Plan
A person saves ₹100 in the first month, ₹150 in the second month, ₹200 in the third month, and so on. The monthly savings form an Arithmetic Progression.

(i) What will be his saving in the 10th month? (1 Mark)
(ii) What will be his total savings in 10 months? (1 Mark)
(iii) In which month will his saving be ₹500? (2 Marks)
[4]