Arithmetic Progression Class 10 MCQ Questions – Maths Class 10 MCQ Online Test are covered in this Article. Arithmetic Progression Class 10 MCQ Questions Test contains 30 questions. Answers to MCQs on Arithmetic Progression Class 10 Maths are available after clicking on the answer. MCQ Questions for Class 10 with Answers have been made for Class 10 students to help check the concept you have learnt from detailed classroom sessions and application of your knowledge.
| Board | CBSE |
| Textbook | Maths (NCERT) |
| Class | Class 10 |
| Chapter | Chapter 5 Arithmetic Progression |
| Category | MCQ Questions for Class 10 Maths with Answers |
Arithmetic Progression Class 10 MCQ Questions
1. The simple average of a given set of numbers is
(a) Arithmetic Progression
(b) Arithmetic mean
(c) Geometric mean
(d) Average
Answer
Answer: (b) Arithmetic mean
2. List of numbers in which each term is obtained by adding a fixed number to the preceding term except the first term.
(a) Arithmetic Progression
(b) Arithmetic mean
(c) Geometric mean
(d) Average
Answer
Answer: (a) Arithmetic Progression
3. Formula for AP
(a) an = a + (n – 1) d.
(b) an = a + (n + 1) d.
(c) an = (n – 1) d
(d) an = (n + 1) d
Answer
Answer: (a) an = a + (n – 1) d.
4. The common difference in AP can be
(a) Negative or zero
(b) Positive or zero
(c) Positive or negative but cannot be zero
(d) Positive or negative or zero
Answer
Answer: (d) Positive or negative or zero
5. Sequence is not an AP
(a) 1, – 1, – 3, – 5, . . .
(b) 1/3, 5/3, 9/3, 13/3 ,17/3 …………
(c) 4+ √5, 4+ 2√5, 4+ 3√5, 4+ 4√5
(d) – 3, 3, – 3, 3, – 3, . . .
Answer
Answer: (d) – 3, 3, – 3, 3, – 3, . . .
Explanation:
a2 – a1 = 3 – (– 3) = 3 + 3 = 6
a3– a2 = – 3 – 3
= – 6
As a3– a2 ≠ a2 – a1, the given list of numbers does not form an AP.
6. Find AP whose 2nd term is 5 and the 5th term is 20.
(a) 1,5,10,15…..
(b) 5,7,10,12,15,….
(c) 0,5,10,15,……..
(d) 5,10,15,20,….
Answer
Answer: (c) 0,5,10,15,……..
Explanation:
an =a + (n-1) d
a2 = a + (2-1) d = a +d =5
a5 = a+ (5-1) d
= a+ 4d =20
By solving, a =0, d=5
AP formed, 0,5,10,15,20………
7. Find the value of a and d ; 1,-1,-3,-5,……
(a) a = 2, d = -1
(b) a = 1, d = -1
(c) a = 1, d = -2
(d) a = -2, d = 1
Answer
Answer: (c) a = 1, d = -2
Explanation:
first term = a = 1
d = a2 – a1
= -1 – 1 = -2
8. Each number in the list of AP is known as
(a) Common difference
(b) Term
(c) Mean
(d) (n-1) term
Answer
Answer: (b) Term
Arithmetic Progression Class 10 MCQ Questions
9. Find the 7th term of the AP, 4+ √5, 4+ 2√5, 4+ 3√5, 4+ 4√5,…….
(a) 4 + 5√5
(b) 4 + 6√5
(c) 4 + 7√5
(d) 4 + 8√5
Answer
Answer: (c) 4 + 7√5
Explanation:
an = a + (n-1) d
d = (4 + 2√5) – (4 + √5) = √5
a7 = (4+ √5) + (7-1) √5
= 4 +√5 + 6√5
= 4 + 7√5
10. In AP, am represents
(a) (n-1)th term
(b) nth term
(c) Last term
(d) General term
Answer
Answer: (c) Last term
11. Find how many terms are there in AP; 18,15,12,………..,-81.
(a) 34
(b) 30
(c) 35
(d) 36
Answer
Answer: (a) 34
Explanation:
a = 18,
d = 15-18 = -3,
l = -81
l = a + (n-1) d
-81 = 18 + (n-1) (-3)
= 18 + 3 – 3n
-3n = -81 -21 = – 102
n = 34
12. In an AP, if d = 3 + √3, n = 7, an= 10 + 6√3, then a is
(a) √3
(b) 6 + √3
(c) 8+ √3
(d) -8
Answer
Answer: (d) -8
Explanation:
an =a + (n-1) d
10 + 6√3 = a + (7 -1) (3 + √3)
10 + 6√3 = a + 6 (3 + √3)
10 + 6√3 = a + 18 + 6√3
a = -8
13. AP having last term is known as
(a) General AP
(b) Finite AP
(c) Infinite AP
(d) All of the above
Answer
Answer: (b) Finite AP
14. Find 10th term of AP, where a1 = 7/2 and a2 = 5
(a) 33/2
(b) 17/2
(c) 15/2
(d) None of the above
Answer
Answer: (d) None of the above
Explanation:
d = a2 – a1 = 5 – 7/2 = 3/2
an =a + (n-1) d
a10 = 7/2 + (10-1)3/2 = 7/2 + 9 x 3/2
= 7/2 + 27/2 = 34/2 = 17
15. If d = √5, Find a13 – a7
(a) 12√5
(b) 6√5
(c) 7- √5
(d) 7 + √5
Answer
Answer: (b) 6√5
Explanation:
a13 – a7 = [ a + 12d] – [ a + 6d]
= 6d = 6√5
16. Sum of the first n terms of an AP is
(a) n/2(a + an)
(b) a + (n-1) d
(c) 2a + (n-1) d
(d) n/2 (a + nd)
Answer
Answer: (a) n/2(a + an)
Explanation:
Sn = (n)/2[ 2a+(n-1)d]
= n/2 [ a+ a+(n-1)d]
=n/2 [ a + an]
Arithmetic Progression Class 10 MCQ Questions
17. Find 10th term of AP, S10 = 45 and S9 = 42
(a) 5
(b) 4
(c) 3
(d) 2
Answer
Answer: (c) 3
Explanation:
an = Sn – Sn-1
a10 = S10 – S9
= 45-42 = 3
18. The middle most term (s) of the AP; 21,19,17, …, -55 is:
(a) 12
(b) 0
(c) -20
(d) -17
Answer
Answer: (d) -17
Explanation:
a = 21,
d = 19-21 = -2,
l = -55
l = a + (n-1) d
-55 = 21 + (n-1) (-2)
= 21 +2 -2n = 23 -2n
-2n = -55-23 = – 78
n = 39;
39 is an odd no. So, middle term n+1/2 = 20th term
a20 = 21 + (20-1) (-2) = 21 – 19×2 = 21-38 = -17
19. If a = 8, an= 62, Sn= 210, find n.
(a) 5
(b) 6
(c) 10
(d) 11
Answer
Answer: (b) 6
Explanation:
Sn = n/2 (a + an )
210 = n/2 (8 + 62)
n = 420/ 70 = 6
20. Next term of the AP √3, 3√3, 5√3, ……. is
(a) 6√3
(b) 7√3
(c) 8√3
(d) 9√3
Answer
Answer: (b) 7√3
Explanation:
a = √3, d = 3√3 – √3 = 2√3
a4 = √3 + (4-1)2√3
= √3 + 6√3 = 7√3
21. The sum of first ten whole number is
(a) 30
(b) 35
(c) 45
(d) 55
Answer
Answer: (c) 45
Explanation:
AP will be: 0, 1, 2, 3,4,5,6,7,8,9
S10 = n/2 (a + l)
= 10/2 (0 + 9) = 5 × 9 = 45
22. If a = 10, l = 81, Sn = 910. find no of terms
(a) 5
(b) 10
(c) 15
(d) 20
Answer
Answer: (d) 20
Explanation:
Sn = n/2 (a + l)
910 = n/2 (10 + 81)
910 × 2 = 91n
n = 20
23. If 2x, x + 10, 3x + 2 are in A.P., find d
(a) 10
(b) 8
(c) 6
(d) 4
Answer
Answer: (d) 4
Explanation:
a =2x
D = a2– a1 = x+10 -2x = 10 -x
D = a3– a2 = (3x +2) -(x + 10)
= 3x + 2- x -10 = 2x – 8
Therefore, 10 – x = 2x -8
3x = 18
X = 6
d = 10-6 = 4
24. If AP is 14, 21, 28…..98. Find n
(a) 12
(b) 13
(c) 14
(d) 15
Answer
Answer: (b) 13
Explanation:
an =a + (n-1) d
a = 14; d=7; an = 98
98 = 14 +(n-1)7
98-14 = (n-1)7
84 /7 = n-1
n = 13
25. If AP: 5, 8, 11, . . . , check whether any 300 term exist or not ?
(a) True
(b) False
Answer
Answer: (b) False
Explanation:
an =a + (n-1) d
a2 = 8; a=5; d=3,
let nth be the 300 term i.e. an =300
300= 5+(n-1) (3)
n=298 / 3
n should be a positive integer hence nth term will not be 300
Arithmetic Progression Class 10 MCQ Questions
26. Write AP, whose 3rd term is 4 and the 7th term is 12.
(a) 7, 6, 5, 4, . . .
(b) 1/3, 5/3, 9/3 ,13/3, 17/3 …………
(c) 4+ √5, 4+ 2√5, 4+ 3√5, 4+ 4√5
(d) 0, 2, 4, 6……….
Answer
Answer: (d) 0, 2, 4, 6……….
Explanation:
an =a + (n-1) d
a2 = a + (3 – 1) d = a + 2d = 4
and a7 = a + (7 – 1) d = a + 6d = 12
4-2d+6d = 12;
hence d= 2; a=0
AP: 0,2,4,6……………
27. In an AP: 20, 18, 16, . . .-40, whether any 0 term exist or not?
(a) True
(b) False
Answer
Answer: (a) True
Explanation:
an =a + (n-1) d
here a2 = 18; a=20; d=-2,
let nth be the 0 term i.e. an =0
0= 20+(n-1) (-2)
0= 20 -2n+2
0= 22 -2n
n = 11
So, 11th term will be 0.
28. Find d, in 0, -3, -6, -9…………..
(a) 3
(b) -3
(c) 6
(d) -6
Answer
Answer: (b) -3
Explanation:
d = -3-0 = -3
29. In an AP, if d = √3, n = 10, an= 10√3, then a is
(a) √3
(b) 6 + √3
(c) 8+ √3
(d) 8
Answer
Answer: (a) √3
Explanation:
an =a + (n-1) d
10√3 = a + (10 -1) (√3) = a + 9√3
a = √3
30. Find 8th term of AP, S8 = 50 and S7 = 42
(a) 10
(b) 8
(c) 6
(d) 4
Answer
Answer: (b) 8
Explanation:
an = Sn – Sn-1
a8 = S8 – S7
= 50-42 = 8
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Frequently Asked Questions on Arithmetic Progression Class 10 MCQ Questions
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Yes . There are 30 MCQ’s on this Chapter in this blog.
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