CBSE Class 10 Mathematics Arithmetic Progression MCQs Set L

Question. Find the general term of the series 4, 7, 10, 13......
(a) \( 3n - 7 \)
(b) \( 3n + 7 \)
(c) \( 3n + 1 \)
(d) \( 3n - 1 \)
Answer: C

Question. Which is the first negative term of the arithmetic progression 35, 30, 25,.....?
(a) 7th term
(b) 5th term
(c) 9th term
(d) 11th term
Answer: C

Question. Find the next term of the arithmetic progression \( \sqrt{12}, \sqrt{27}, \sqrt{48} \)
(a) \( \sqrt{75} \)
(b) \( \sqrt{60} \)
(c) \( \sqrt{80} \)
(d) \( \sqrt{90} \)
Answer: A

Question. What is the term of an arithmetic progression whose sum to 'n' terms is \( 2n^2 - 3n \)?
(a) \( 4n - 3 \)
(b) \( 4n - 5 \)
(c) \( 4n + 5 \)
(d) \( 5 - 4n \)
Answer: B

Question. Which term of the arithmetic progression 30, 27, 24,.... is 0?
(a) 8th term
(b) 10th term
(c) 13th term
(d) 11th term
Answer: D

Question. The numbers 28, 22, 'x', 'y', 4 are in arithmetic progression. What are the respective values of 'x' and 'y'?
(a) 10, 16
(b) 20, 18
(c) 18, 16
(d) 16, 10
Answer: D

Question. What is the sum to 'n' terms of the series \( \sqrt{5}, \sqrt{20}, \sqrt{45}, \sqrt{80},..... \)?
(a) \( \frac{n(n+1)\sqrt{5}}{2} \)
(b) \( \frac{n(n+1)}{\sqrt{2}} \)
(c) \( \frac{n}{2} \left( \frac{n+1}{\sqrt{5}} \right) \)
(d) \( n(n+1)\sqrt{5} \)
Answer: A

Question. What is the sum of the first 'n' even numbers?
(a) \( n^2 + 1 \)
(b) \( n(n - 1) \)
(c) \( n^2 - n \)
(d) \( n(n + 1) \)
Answer: D

Question. What is the sum of first 'n' odd numbers starting from 11?
(a) \( n^2 + 10n \)
(b) \( n^2 - 10n \)
(c) \( 10n - n^2 \)
(d) \( n^2 \)
Answer: A

Question. How many two digit numbers are divisible by 4?
(a) 20
(b) 16
(c) 25
(d) 22
Answer: D

Question. How many terms of the arithmetic progression 1, 9, 17, .... must be taken to give a sum of 1540?
(a) 10
(b) 40
(c) 20
(d) 15
Answer: C

Question. What is the sum of 36 terms of the series whose \( n^{th} \) term is \( 5n + 4 \)?
(a) 4347
(b) 3474
(c) 4374
(d) 3447
Answer: B

Question. Divide 21 into three parts that are in arithmetic progression and whose product is 168.
(a) 3, 6, 9
(b) 14, 17, 11
(c) 2, 6, 14
(d) 2, 7, 12
Answer: D

Question. Which term of the arithmetic progression 3, 8, 13, ..... is 55 more than its 20th term?
(a) 29th term
(b) 31st term
(c) 25th term
(d) 27th term
Answer: B

Question. Identify the formula for the \( n^{th} \) term of the arithmetic progression whose first term, (a) is 2 - x, and the common difference, (d) is 'x'.
(a) \( 2 + x - nx \)
(b) \( 2 + (n - 2)x \)
(c) \( 2 - x - nx \)
(d) \( 2 + (n - 1)x \)
Answer: B

Question. Find the number of terms of the arithmetic progression \( \frac{1}{3}, \frac{1}{2}, \frac{2}{3}, ...... \frac{11}{6} \)
(a) 8
(b) 10
(c) 12
(d) 13
Answer: B

Question. The first, second and last terms of an arithmetic progression are 5, 9 and 101 respectively. Find the number of terms in the arithmetic progression.
(a) 30
(b) 50
(c) 25
(d) 75
Answer: C

Question. Find the sum of the first 18 terms, of the arithmetic progression 12b, 8b, 4b,......
(a) 126b
(b) -56b
(c) 256b
(d) -288b
Answer: D

Question. Find the sum of the arithmetic progression, \( x - 2y, 2x - y, 3x, ...... 11x + 8y \).
(a) \( 33(2x + y) \)
(b) \( 22(2x + y) \)
(c) \( 28(x + y) \)
(d) \( 33x + 11y \)
Answer: A

Question. Find the sum from the sixth term to the twelfth term of the arithmetic progression 6, 10, 14, ....
(a) 176
(b) 232
(c) 266
(d) 184
Answer: C

Question. The first term and the common difference of an arithmetic progression are 13 and 5 respectively. Find the sum from the 6th term to the 20th term.
(a) 876
(b) 146
(c) 1095
(d) 1080
Answer: C

Question. Find the value of 'n' if the sum of the first 'n' terms of the A.P. 5, 23, 31, ....... is 708.
(a) 9
(b) 8
(c) 12
(d) 10
Answer: C

Question. An arithmetic progression has a 3rd term of 13 and a last term of 148. If the common difference is 5, find the number of terms of the progression.
(a) 30
(b) 40
(c) 50
(d) 75
Answer: A

Question. Given that the sum of the first 'n' terms of an arithmetic progression is \( 2n^2 + 3n \), find the twelfth term.
(a) \( 7^2 \)
(b) 36
(c) \( \sqrt{625} \)
(d) 56
Answer: A

Question. The first two terms of an arithmetic progression are 27 and 24 respectively. How many terms of the progression are to be added to get - 30?
(a) 15
(b) 20
(c) 25
(d) 18
Answer: B

Question. A secondary school had an enrolment of 1620 students in the year 2009 which increases by 150 students per year. What was the enrolment in the year 2013?
(a) 2170
(b) 2070
(c) 2220
(d) 2150
Answer: C

Question. A cineplex has 13 rows of seats with 10 seats in the first row, 12 in the second, 14 in the third and so on. What is the total number of seats in the cineplex?
(a) 252
(b) 256
(c) 258
(d) 286
Answer: D

Question. Sulekha intends to read a 200 page book within a specific period-She starts by reading 11 pages on the first day and increases her rate of reading by reading an extra 2 pages for each subsequent day How long will she take to finish reading the book?
(a) 20
(b) 10
(c) 15
(d) 25
Answer: B

Question. The 6th term of an arithmetic progression is 30 and the sum of the first six terms is 210. Find the sum of the next 6 consecutive terms.
(a) 100
(b) 50
(c) 138
(d) 204
Answer: C

Question. In an arithmetic progression, the fourth term is 8 and the sum of 12 terms is 156. Find the value of 'p' if the \( p^{th} \) term is 1000.
(a) 200
(b) 500
(c) 300
(d) 100
Answer: B

Question. A circle is divided into 18 sectors such that the angles subtended at the centre form an arithmetic progression. Given that the angle of the smallest sector is \( 11.5^\circ \), find the angle of the biggest sector.
(a) \( 30^\circ \)
(b) \( 15.5^\circ \)
(c) \( 45^\circ \)
(d) \( 28.5^\circ \)
Answer: D

Question. An arithmetic progression has 10 terms. The sum of the odd terms is 245 whereas the sum of the even terms is 305. Find the common difference.
(a) 2
(b) 7
(c) 3
(d) 1
Answer: D

Question. Given an arithmetic progression -10,-5, 0,..... Identify three consecutive terms of the progression whose sum is 90.
(a) 26, 31, 36
(b) 25, 30, 35
(c) 20, 30, 40
(d) 18, 23, 28
Answer: B

Question. The first three terms of a sequence are 8, 'y' and 18. Find the positive value of 'y' so that the sequence is an arithmetic progression.
(a) 26
(b) 18
(c) 12
(d) 13
Answer: D

Question. The sum of the first 10 terms of an arithmetic progression is four times the sum of its first five terms. Find the ratio of the first term to the common difference.
(a) 1:4
(b) 4:1
(c) 2:1
(d) 1:2
Answer: D

Question. How many numbers between 100 and 1000 are divisible by 7?
(a) 7
(b) 128
(c) 132
(d) 127
Answer: B

Question. Find the sum of 14 AM's between 5 and 8.
(a) 91
(b) 89
(c) 90
(d) 85
Answer: A

Question. If \( 1^3 + 2^3 + ..... + m^3 = 3025 \), find m.
(a) 12
(b) 10
(c) 17
(d) 12
Answer: B

Question. If \( m^{th} \) term of an arithmetic progression is 'n' and \( n^{th} \) term is 'm', find its \( (m + n)^{th} \) term.
(a) 0
(b) \( m + n - p \)
(c) \( m + n \)
(d) \( \frac{mn}{m + n} \)
Answer: A

Question. The sum to 'n' natural numbers is \( S_1 \), sum of the squares of 'n' natural numbers is \( S_2 \) and sum of the cubes of 'n' natural numbers is \( S_3 \). Which of the following is equal to \( 9S_2^2 \)?
(a) \( S_1(1 - 8S_2) \)
(b) \( S_3(1 + 8S_1) \)
(c) \( S_1S_2(1 + 8S_2) \)
(d) \( S_1S_3(1 - 8S_3) \)
Answer: B

Question. In an arithmetic progression if 7 times the 7th term is equal to 11 times the 11th term, find its 18th term.
(a) 1
(b) 0
(c) -1
(d) 2
Answer: B

Question. Find the sum of the numbers in between 1 and 1000 which are divisible by 9.
(a) 55944
(b) 54954
(c) 99994
(d) 99894
Answer: A

Question. There are 'n' arithmetic means in between 'a' and 'b'. Find the common difference.
(a) \( \frac{b - a}{n + 1} \)
(b) \( \frac{b + a}{n - 1} \)
(c) \( \frac{b - a}{n - 1} \)
(d) \( \frac{b + a}{n + 1} \)
Answer: A

Question. What is the sum of 'n' arithmetic means between 'a' and 'b'?
(a) \( \frac{3}{2}(a + 2b) \)
(b) \( \frac{n}{2}[a + b] \)
(c) \( \frac{n}{2}[a - b] \)
(d) \( \frac{n}{4}[a + b] \)
Answer: B

Question. Find the sum of \( (1 - \frac{1}{n}) + (1 - \frac{2}{n}) + (1 - \frac{3}{n}) .... \) n terms.
(a) \( \frac{n}{2} \)
(b) \( \frac{n - 1}{2} \)
(c) \( \frac{n + 1}{2} \)
(d) \( \frac{n(n + 1)}{n^2} \)
Answer: B

Question. In an arithmetic progression, if \( t_p = q, t_q = p \), find \( t_{pq} \).
(a) \( p + q - pq \)
(b) \( p + q \)
(c) \( p - q + pq \)
(d) \( pq - p - q \)
Answer: A

Question. Find three numbers in arithmetic progression whose sum is 3 and product is 35.
(a) 1, 5, 7
(b) -5, 7, -1
(c) -5, 1, 7
(d) -7, 5, -1
Answer: C

Question. Which of the following is incorrect?
(a) \( S_n \) of the arithmetic progression 3, 13, 23,.... is \( 5n^2 - 8n \).
(b) \( S_n = 3n^2 - 8n \) is the sum of an arithmetic progression whose common difference is 6.
(c) \( n^{th} \) term, \( t_n = s_n - s_{n-1} \)
(d) The \( n^{th} \) term of an arithmetic progression is \( t_n = a + (n - 1)d \).
Answer: A

Question. Given \( P = 3 + 5 + 7 + \dots \) (n terms) and \( Q = 5 + 8 + 11 + \dots \) (10 terms). What is the value of 'n' if \( \frac{P}{Q} = 7 \)?
(a) 25
(b) 35
(c) 30
(d) 20
Answer: B

Question. What is the value of 'x' if \( 2x, x + 10 \) and \( 3x + 2 \) are in arithmetic progression?
(a) 5
(b) 6
(c) 4
(d) -6
Answer: B

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