CBSE Class 10 Mathematics Arithmetic Progressions Worksheet Set C

Question. Which of the following form of an AP?
(a) − 1, − 1, − 1, − 1, ...
(b) 0, 2, 0, 2, …
(c) 1, 1, 2, 2, 3, 3
(d) 1/2, 1/3, 1/4
Answer : A

Question. The common difference of an AP, whose nth term is an =(3n + 7), is
(a) 3
(b) 7
(c) 10
(d) 6
Answer : A

Question. The first four terms of an AP whose first term is − 2 and the common difference is −2, are
(a) − 2, 0, 2, 4
(b) − 2, 4, − 8, 16
(c) − 2, − 4, − 6, − 8
(d) − 2, − 4, − 8, − 16
Answer : C

Question. Which of the following is not an AP?
(a) −12 . , 0.8, 2.8, ...
(b) 3, 3 + √2, 3 +2 √2, 3 + 3√2, …
(c) 4/3, 7/3, 9/3, 12/3 .... 
(d) −1/5, −2/5, −3/5 .... 
Answer : C

Question. If − (5/7), a,2 are consecutive terms in an Arithmetic Progression, then the value of ‘a’ is
(a) 9/7
(b) 9/14
(c) 19/7
(d) 19/14
Answer : B

Question.  Let a be a sequence defined by a₁ = 1, a₂ = 1 and an = a_n − 1 + a_n − 2 for all n > 2, then the value of a₄/a₃ is
(a) 2/3
(b) 5/4
(c) 4/5
(d) 3/2
Answer : D

Question. The 11^th term of an AP −5, −5/2, 0, 5/2, , , ,...
(a) − 20
(b) 20
(c) −30
(d) 30
Answer : B

Question. The value of x for which 2x,(x + 10) and (3x + 2) arethe three consecutive terms of an AP, is
(a) 6
(b) − 6
(c) 18
(d) −18
Answer : A

Question.  The value of p for which (2p + 1), 10 and (5p + 5) are three consecutive terms of an AP is
(a) − 1
(b) − 2
(c) 1
(d) 2
Answer : C

Question. The 21st term of an AP whose first two terms are − 3 and 4, is
(a) 17
(b) 137
(c) 143
(d) − 143
Answer : B

Question.  If the common difference of an AP is 5, then what is a18 − a13?
(a) 5
(b) 20
(c) 25
(d) 30
Answer : C

Question. If an AP have 8 as the first term and −5 as the common difference and its first three terms are 8, A,B, then (A +B) is equal to
(a) 0
(b) −1
(c) 1
(d) 2
Answer : C

Question. In an AP, if d = −4, n = 7 and a_n = 4, then a is equal to
(a) 6
(b) 7
(c) 20
(d) 28
Answer : D

Question. Which term of an AP : 21, 42, 63, 84, ... is 210?
(a) 9th
(b) 10th
(c) 11th
(d) 12th
Answer : B

Question. If the first term of an AP is − 5 and the common difference is 2, then the sum of the first 6 terms is
(a) 0
(b) 5
(c) 6
(d) 15
Answer : A

Question.  In an AP, if a = 1, a_n = 20 and S_n = 399, then n is equal to
(a) 19
(b) 21
(c) 38
(d) 42
Answer : C

Question.  What is the common difference of an AP in which a₁₈ − a₁₄ = 32 ?
(a) 8
(b) − 8
(c) − 4
(d) 4
Answer : A

Question. Which term of the AP 5, 15, 25, ... will be 130 more than its 31st term?
(a) 42
(b) 44
(c) 46
(d) 48
Answer : B

Question.  If the 2nd term of an AP is 13 and 5th term is 25, what is its 7th term?
(a) 30
(b) 33
(c) 37
(d) 38
Answer : B

Question. The number of terms of an AP 5, 9, 13, ..., 185 is
(a) 31
(b) 51
(c) 41
(d) 46
Answer : D

Question. The sum of AP, sequence −37, − 33, − 29, . . . . . . . . . upto 12 term is
(a) 180
(b) −180
(c) 170
(d) −170
Answer : B

Question. Two APs have the same common difference. The first term of one of these is − 1 and that of the other is − 8. The difference between their 4th terms is [NCERT Exemplar]
(a) − 1
(b) − 8
(c) 7
(d) − 9
Answer : C

Question. If 7 times the 7th term of an AP is equal to 11 times its 11th term, then its 18th term will be
(a) 7
(b) 11
(c) 18
(d) 0
Answer : D

Question. The 4th term from the end of an AP − 11 , − 8, − 5, . . . , 49 is
(a) 37
(b) 40
(c) 43
(d) 58
Answer : B

Question. The sum of first 16 terms of the AP 10, 6, 2, ... is
(a) − 320
(b) 320
(c) − 352
(d) − 400
Answer : A

Question.  The sum of first five multiples of 3 is
(a) 45
(b) 55
(c) 65
(d) 75
Answer : A

Answer the following:

Question. Find the sum of first 10 terms of the AP: 2, 7, 12, ... 
Answer : 245

Question. If the sum of first m terms of an AP is 2 m² + 3 m, then what is its second term? 
Answer : 9

Question. Find the sum of first 10 multiples of 6.
Answer : First 10 multiples of 6 are 6, 12, 18, ....., 60.
This is an AP in which a = 6, n = 10 and d = 6.
∴ Sum of first 10 multiples of 6 = S10
⇒ S₁₀ = n/2 [2a + (n - 1) d]
= 10/2 [2×6 + ]10 – 1)6]
= 5 (12 + 54)
= 5 × 66 = 330

Question. What is the sum of five positive integers divisible by 6? 
Answer : 90

Question. If the sum of the first q terms of an AP is 2q + 3q², what is its common difference? 
Answer : Given that,
S_q = 2q + 3q²
S₁ = 2 + 3 = 5 = T₁ = First term            [put q = 1]
S₂ = 4 + 3(4) = 16                                 [put q = 2]
S₃ = 6 + 3(9) = 33                                 [put q = 3
∴ 2^nd term,
T₂ = S₂ – S₁ = 16 – 5 = 11
∴ 3^rd term,
T₃ = S₃ – S₂ = 33 – 16 = 17
Common difference
= T₃ – T₂ = 17 – 11 = 6

Question. If nth term of an AP is (2n + 1), what is the sum of its first three terms? 
Answer : a₁ = 3, a₃ = 7, S₃ = 3/2 (3 + 7) = 15

Question. Find the sum of first 100 natural numbers.
Answer : Natural numbers are 1, 2, 3, 4, ...
The sum of first 100 natural numbers is given by
S_n = n(n + 1)/2 = 100 x (100 + 1)/2
= 100 x 101 / 2
= 50 × 101 = 5050

Short Answer type Questions

Please click on below link to download CBSE Class 10 Mathematics Arithmetic Progressions Worksheet Set C