CBSE Class 10 Mathematics Arithmetic Progression Assignment Set 01

Question. The value of x for which 2x, (x + 10) and (3x + 2) are the three consecutive terms of an AP, is
(a) 6
(b) -6
(c) 18
(d) -18

Answer: A

Question. The first term of 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

Answer: C

Question. The n^th term of the AP a , 3a , 5a , ... is
(a) na
(b) (2n - 1)a
(c) (2n + 1)a
(d) 2na

Answer: B

Question. The common difference of the AP 1/p, 1 - p / p , 1 - 2p / p, ... is
(a) 1
(b) p/1
(c) - 1
(d) - (1/p)

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. In an AP, if a = 3.5, d = 0 and n = 101, then an will be
(a) 0
(b) 3.5
(c) 103.5
(d) 104.5

Answer: B

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 common difference of an AP is 5, then what is a₁₈- a₁₃?
(a) 5
(b) 20
(c) 25
(d) 30

Answer: C

Question. The 11th term of an AP -5,  -5/2 , 0, 5/2 , ....., is
(a) -20
(b) 20
(c) -30
(d) 30

Answer: B

Question. In an AP, if a = 3.5, d = 0 and n = 101, then an will be
(a) 0
(b) 3.5
(c) 103.5
(d) 104.5

Answer: B

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. 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. In an AP, if a = 1, an = 20 and Sn = 399, then n is equal to
(a) 19
(b) 21
(c) 38
(d) 42

Answer: C

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

Answer: A

Question. If the sum of the series 2 + 5 + 8 + 11 .......... is 60100, then the number of terms are
(a) 100
(b) 200
(c) 150
(d) 250

Answer: B

Question. If the nth term of an AP is given by a_n = 5n − 3, then the sum of first 10 terms if
(a) 225
(b) 245
(c) 255
(d) 270

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. Then the difference between their 4th terms is
(a) -1
(b) -8
(c) 7
(d) -9

Answer: C

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. There are 60 terms is an AP of which the first term is 8 and the last term is 185. The 31^st term is
(a) 56
(b) 94
(c) 85
(d) 98

Answer: D

Question. An AP starts with a positive fraction and every alternate term is an integer. If the sum of the first 11 terms is 33, then the fourth term is
(a) 2
(b) 3
(c) 5
(d) 6

Answer: A

Question. If the sum of the first 2n terms of 2, 5, 8, .......... is equal to the sum of the first n terms of 57, 59, 61, .........., then n is equal to
(a) 10
(b) 12
(c) 11
(d) 13

Answer: C

Question. The 21th term of an AP whose first two terms are -3 and 4, is
(a) 17
(b) 137
(c) 143
(d) -143

Answer: B

Question. The number of two digit numbers which are divisible by 3 is
(a) 33
(b) 31
(c) 30
(d) 29

Answer: C

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

Answer: D

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. The list of numbers -10, -6, -2, 2, ..... is
(a) an AP with d =− 16
(b) an AP with d = 4
(c) an AP with d =− 4
(d) not an AP

Answer: B

Question. If the n^th term of an AP is 4n + 1, then the common difference is
(a) 3
(b) 4
(c) 5
(d) 6

Answer: B

Question. The sum of 11 terms of an AP whose middle term is 30, is
(a) 320
(b) 330
(c) 340
(d) 350

Answer: B

Question. Five distinct positive integers are in a arithmetic progression with a positive common difference. If their sum is 10020, then the smallest possible value of the last term is
(a) 2002
(b) 2004
(c) 2006
(d) 2007

Answer: C

Question. If a,b, c,d,e, f are in AP, then e - c is equal to
(a) 2(c - a)
(b) 2(d - c
(c) 2(f - d)
(d) (d - c)

Answer: B

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

Answer: D

Question. If the 2^nd 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

Fill In The Blanks

Question. In an AP, the letter d is generally used to denote the ..........
Answer: common difference

Question. If a and d are respectively the first term and the common difference of an AP, a + 10d , denotes the .......... term of the AP.
Answer: eleventh

Question. An arithmetic progression is a list of numbers in which each term is obtained by .......... a fixed number to the preceding term except the first term.
Answer: adding

Question. If Sn denotes the sum of n term of an AP, then S₁₂- S₁₁ is the .......... term of the AP.
Answer: twelfth

Question. The nth term of an AP whose first term is a and common difference is d is ..........
Answer: a + (n − 1)d

Question. The nth term of an AP is always a .......... expression.
Answer: linear

Question. The difference of corresponding terms of two AP’s will be ..........
Answer: another AP

Question. Write the first four terms of the sequence defined by \( t_n = n(n+1) \)
Answer: \( 2, 6, 12, 20 \)

Question. Write the first three terms of the sequence \( a_n = (n^2+1) \)
Answer: \( 2, 5, 10 \)

Question. Write the 6th term from the sequence \( t_n = \frac{1 + (-2)^n}{n-1} \)
Answer: \( 13 \)

Question. Write the 5th term from the sequence \( a_n = \frac{(n+1)(n+2)}{n+3} \)
Answer: \( \frac{21}{4} \)

Question. Write and find the 5th term of an AP whose 1st term is 3 and Common difference is 5.
Answer: \( 23 \)

Question. Find an A.P. whose nth term is \( (2n+5) \)
Answer: \( 7, 9, 11, \dots \)

Question. Find an AP whose general term is \( \frac{3n-2}{2} \)
Answer: \( \frac{1}{2}, 2, \frac{7}{2}, \dots \)

Question. The first term of an AP is 5 and Common difference is -3. Find 11th term of the A-P
Answer: \( -25 \)

Question. Find the 12th term and general term of the A-P. 5, 8, 11, 14, \dots
Answer: \( t_{12} = 38 \), \( t_n = 3n+2 \)

Question. Which term of the AP 1, 6, 11, 16, \dots is 81
Answer: 17th

Question. The 4th term of an A.P is 14 and its 8th term is 30. Find the first term and the Common difference.
Answer: \( a = 2, d = 4 \)

Question. Which term of the sequence 45, 41, 37, 33, \dots is the 1st negative term?
Answer: 13th is the 1st negative term.