Arithmetic Progressions: 1 mark Questions (CBSE Class 10)

The sum of first n terms of an A.P. is $50\sqrt{2}$. If the first and the last terms are $\sqrt{2}$ and $19\sqrt{2}$ respectively, then the value of n is :

1. (A)10
2. (B)5
3. (C)15
4. (D)20

$n^{th}$ term of the A.P. $-\frac{3}{2},\frac{3}{2},\frac{9}{2}$, ... is :

1. (A)$\frac{3n}{2}-3$
2. (B)$3n-\frac{9}{2}$
3. (C)$\frac{3n-9}{2}$
4. (D)$3n+\frac{3}{2}$

$n^{th}$ term of an A.P. is 5n – 15. The common difference of the A.P. is :

1. (A)5n
2. (B)5
3. (C)– 5
4. (D)10

$n^{th}$ term of the A.P. : $\frac{-1}{3},\frac{4}{3},3,\dots$ is

1. (A)$\frac{5n-9}{3}$
2. (B)$\frac{5n-6}{3}$
3. (C)$\frac{3n-4}{3}$
4. (D)$\frac{3n+2}{3}$

If $-26,x,2$ are in A.P., then the value of $x$ is

1. (A)14
2. (B)$-13$
3. (C)$-12$
4. (D)$-14$

If $\frac{-20}{9},\frac{-2}{9},\frac{16}{9},\dots$ are in A.P., then next term of the sequence is

1. (A)$\frac{32}{9}$
2. (B)$\frac{46}{9}$
3. (C)$\frac{2}{9}$
4. (D)$\frac{34}{9}$

If $14^{th}$ term of an A.P. is 4 and its $15^{th}$ term is zero, then its first term is

1. (A)$-48$
2. (B)$-56$
3. (C)56
4. (D)48

The common difference of the AP : $\sqrt{2},2\sqrt{2},3\sqrt{2},4\sqrt{2},.....$ is :

1. (A)$\sqrt{2}$
2. (B)1
3. (C)$2\sqrt{2}$
4. (D)$-\sqrt{2}$

The first term of an AP is $p$ and the common difference is $q$, then its 10th term is :

1. (A)$q-9p$
2. (B)$p-9q$
3. (C)$p+9q$
4. (D)$2p+9q$

Which of the following sequence is not an A.P. ?

1. (A)$2,\frac{5}{2},3,\frac{7}{2},...$
2. (B)$-1.2,-3.2,-5.2,-7.2,...$
3. (C)$\sqrt{2},\sqrt{8},\sqrt{18},...$
4. (D)$1^2,3^2,5^2,7^2,...$

Assertion (A) : The mean of first 'n' natural numbers is $\frac{n-1}{2}$.
Reason (R): The sum of first 'n' natural numbers is $\frac{n(n+1)}{2}$.

1. (A)Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
2. (B)Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
3. (C)Assertion (A) is true, but Reason (R) is false.
4. (D)Assertion (A) is false, but Reason (R) is true.

The value of x for which 2x, (x + 10) and (3x + 2) are the three consecutive terms of an A.P. is :

1. (A)6
2. (B)$-6$
3. (C)18
4. (D)$-18$

The number of multiples of 4 lying between 12 and 250 is :

1. (A)59
2. (B)59.5
3. (C)60
4. (D)61

The $n^{th}$ term of the A.P. $\frac{-1}{3},\frac{2}{3},\frac{5}{3},\frac{8}{3},...$ is :

1. (A)$3n-4$
2. (B)$n-\frac{4}{3}$
3. (C)$\frac{n-2}{3}$
4. (D)$\frac{n-4}{3}$

The number of multiples of 6 lying between 25 and 363 is :

1. (A)56
2. (B)56.5
3. (C)57
4. (D)58

The $n^{th}$ term of an A.P. is $\sqrt{2}n+1$. Its common difference is

1. (A)$\sqrt{2}$
2. (B)$\sqrt{2}n$
3. (C)1
4. (D)$\sqrt{2}+1$

In an A.P., $a=-3$ and $S_{17}=357$. The value of $a_{17}$ is

1. (A)47
2. (B)39
3. (C)45
4. (D)42

If sum of first ten terms of an A.P. is zero with a as the first term and d, the common difference, which of the following relation is true ?

1. (A)$10a+9d=0$
2. (B)$2a=9d$
3. (C)$a_{10}=-a$
4. (D)$a_{10}=a$

If $a_n$ represents $n^{th}$ term of the A.P. $-\frac{15}{4},-\frac{10}{4},-\frac{5}{4},\dots$ then value of $a_{16}-a_{12}$ is

1. (A)4
2. (B)$\frac{5}{4}$
3. (C)5
4. (D)$\frac{25}{4}$

In an A.P., if $a_{14}-a_8=24$, then the common difference of the A.P. is

1. (A)6
2. (B)4
3. (C)$\pm 4$
4. (D)3

If $n^{th}$ term of an A.P. is $5n-6$, then its common difference is :

1. (A)$-6$
2. (B)$5n$
3. (C)5
4. (D)6

The $20^{th}$ term of the A.P. : $10\sqrt{2},6\sqrt{2},2\sqrt{2},....$ is :

1. (A)$-76+10\sqrt{2}$
2. (B)$-62\sqrt{2}$
3. (C)$-66\sqrt{2}$
4. (D)$86\sqrt{2}$

In an A.P., $a_n-a_{n-4}=32$. Its common difference is :

1. (A)$-8$
2. (B)8
3. (C)$4n$
4. (D)4

$10^{th}$ term of the A.P. : –12, –19, –26, .... is

1. (A)–75
2. (B)–65
3. (C)51
4. (D)–82

The $16^{th}$ term of the A.P. : $5\sqrt{3}$, $2\sqrt{3}$, $-\sqrt{3}$, ... is

1. (A)$-25\sqrt{3}$
2. (B)$-40\sqrt{3}$
3. (C)$50\sqrt{3}$
4. (D)$-45+5\sqrt{3}$

$22^{nd}$ term of the A.P. : $\frac{3}{2},\frac{1}{2},\frac{-1}{2},\frac{-3}{2}$, ........ is

1. (A)$\frac{45}{2}$
2. (B)$-9$
3. (C)$\frac{-39}{2}$
4. (D)$-21$

If the sum of first n terms of an A.P. is given by $S_n=\frac{n}{2}(3n+1)$, then the first term of the A.P. is

1. (A)2
2. (B)$\frac{3}{2}$
3. (C)4
4. (D)$\frac{5}{2}$

$15^{th}$ term of the A.P. $\frac{13}{3},\frac{9}{3},\frac{5}{3}$, ....... is

1. (A)23
2. (B)$\frac{-53}{3}$
3. (C)$-11$
4. (D)$\frac{-43}{3}$

If the sum of first $m$ terms of an AP is $2m^2+3m$, then its second term is :

1. (A)$10$
2. (B)$9$
3. (C)$12$
4. (D)$4$

The $11^{\text{th}}$ and $13^{\text{th}}$ term of an AP are $39$ and $45$, respectively. What is the common difference of the AP ?

1. (A)$42$
2. (B)$21$
3. (C)$6$
4. (D)$3$

The $10^{th}$ term of the AP
$5,\frac{19}{4},\frac{9}{2},\frac{17}{4},\dots$ is :

1. (A)$\frac{11}{4}$
2. (B)$\frac{4}{11}$
3. (C)$\frac{13}{4}$
4. (D)$\frac{4}{13}$

Assertion (A) : Common difference of the AP : $5,1,-3,-7,\dots$ is 4.
Reason (R) : Common difference of the AP : $a_1,a_2,a_3,\dots ,a_n$ is obtained by $d=a_n-a_{n-1}$.

1. (A)Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
2. (B)Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
3. (C)Assertion (A) is true, but Reason (R) is false.
4. (D)Assertion (A) is false, but Reason (R) is true.

The $9^{th}$ term from the end (towards first term) of the AP $7,11,15,19,\dots ,147$ is :

1. (A)135
2. (B)125
3. (C)115
4. (D)39

Assertion (A) : For an A.P., 3,6,9, ..., 198, $10^{\text{th}}$ term from the end is 168.
Reason (R) : If 'a' and '$l$' are the first term and last term of an A.P. with common difference 'd', then $n^{\text{th}}$ term from the end of the given A.P. is $l-(n-1)d$.

1. (A)Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
2. (B)Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of (A).
3. (C)Assertion (A) is true, but Reason (R) is false.
4. (D)Assertion (A) is false, but Reason (R) is true.

In an A.P. ; if $a=8$ and $a_{10}=-19$, then value of $d$ is :

1. (A)3
2. (B)$-\frac{11}{9}$
3. (C)$-\frac{27}{10}$
4. (D)$-3$

In an A.P., if $d=-4$ and $a_7=4$, then the first term ‘a’ is equal to

1. (A)6
2. (B)7
3. (C)20
4. (D)28

If the first term of an AP is $-3$ and common difference $-2$, then the seventh term is

1. (A)$-9$
2. (B)9
3. (C)$-17$
4. (D)$-15$

The common difference of an A.P. whose $n^{th}$ term is given by $a_n=5n-1$, is :

1. (A)1
2. (B)6
3. (C)5
4. (D)4

The $30^{th}$ term of the A.P. $-3,-7,-11,\dots$ is :

1. (A)113
2. (B)$-117$
3. (C)$-119$
4. (D)$-120$

If in an A.P., $a=2$ and $S_{10}=335$, then its $10^{th}$ term is :

1. (A)55
2. (B)65
3. (C)68
4. (D)58

The common difference of an A.P., if $a_{23}-a_{19}=32$, is :

1. (A)$8$
2. (B)$-8$
3. (C)$-4$
4. (D)$4$

Assertion (A) : Common difference of the A.P. $5,1,-3,-7$ .... is 4.
Reason (R) : Common difference of the A.P. $a_1,a_2,a_3$ ...., $a_n$ is obtained by $d=a_n-a_{n-1}$.

1. (A)Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
2. (B)Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of Assertion (A).
3. (C)Assertion (A) is true, but Reason (R) is false.
4. (D)Assertion (A) is false, but Reason (R) is true.

In an A.P., if the first term $a=7$, $n$th term $a_n=84$ and the sum of first $n$ terms $s_n=\frac{2093}{2}$, then $n$ is equal to :

1. (A)22
2. (B)24
3. (C)23
4. (D)26

$n$th term of an A.P. is $7n+4$. The common difference is :

1. (A)$7n$
2. (B)4
3. (C)7
4. (D)1

In an A.P., if the first term $(a)=-16$ and the common difference $(d)=-2$, then the sum of first 10 terms is :

1. (A)$-200$
2. (B)$-70$
3. (C)$-250$
4. (D)250

The common difference of an A.P. in which $a_{15}-a_{11}=48$, is

1. (A)12
2. (B)16
3. (C)$-12$
4. (D)$-16$

Which term of the A.P. $-29,-26,-23,\dots ,61$ is 16 ?

1. (A)$11^{th}$
2. (B)$16^{th}$
3. (C)$10^{th}$
4. (D)$31^{st}$

The sum of first 200 natural numbers is

1. (A)2010
2. (B)2000
3. (C)20100
4. (D)21000

The common difference of an A.P. in which $a_{20}-a_{15}=20$, is

1. (A)4
2. (B)5
3. (C)4d
4. (D)5d

The common difference of the A.P.
$\frac{1}{2x},\frac{1-4x}{2x},\frac{1-8x}{2x}$, ................is :

1. (A)$-2x$
2. (B)$-2$
3. (C)$2$
4. (D)$2x$

If the sum of first n terms of an A.P. is $3n^2+4n$ and its common difference is 6, then its first term is :

1. (A)7
2. (B)4
3. (C)6
4. (D)3

Three numbers in A.P. have the sum 30. What is its middle term ?

1. (A)4
2. (B)10
3. (C)16
4. (D)8

If the first three terms of an A.P. are $3p-1$, $3p+5$, $5p+1$ respectively; then the value of p is :

1. (A)2
2. (B)$-3$
3. (C)4
4. (D)5

The next ($4^{th}$) term of the A.P. $\sqrt{18},\sqrt{50},\sqrt{98},\dots$ is :

1. (A)$\sqrt{128}$
2. (B)$\sqrt{140}$
3. (C)$\sqrt{162}$
4. (D)$\sqrt{200}$

The number of terms in the A.P. 3, 6, 9, 12, ..., 111 is :

1. (A)36
2. (B)40
3. (C)37
4. (D)30

The next ($4^{th}$) term of the A.P. $\sqrt{7},\sqrt{28},\sqrt{63},\dots$ is :

1. (A)$\sqrt{70}$
2. (B)$\sqrt{84}$
3. (C)$\sqrt{97}$
4. (D)$\sqrt{112}$

The $14^{th}$ term from the end of the A.P. –11, –8, –5, ..., 49 is :

1. (A)7
2. (B)10
3. (C)13
4. (D)28

The seventh term of an A.P. whose first term is 28 and common difference $-4$, is

1. (A)0
2. (B)4
3. (C)52
4. (D)56

In an AP, if $d=-4$, $n=7$ and $a_n=4$, then the value of a is

1. (A)6
2. (B)7
3. (C)20
4. (D)28

How many terms are there in the A.P. given below ?
14, 19, 24, 29, ....., 119

1. (A)18
2. (B)14
3. (C)22
4. (D)21

The sum of the first 21 terms of an A.P. : 16, 12, 8, 4, ..... is :

1. (A)$-480$
2. (B)$-504$
3. (C)1176
4. (D)$-484$

The $8^{th}$ term of an A.P. is 17 and its $14^{th}$ term is 29. The common difference of this A.P. is :

1. (A)3
2. (B)2
3. (C)5
4. (D)$-2$

The sum of the first 100 even natural numbers is :

1. (A)10100
2. (B)2550
3. (C)5050
4. (D)10010

The sum of the first 50 odd natural numbers is :

1. (A)5000
2. (B)2500
3. (C)2550
4. (D)5050

If $-5,x,3$ are three consecutive terms of an A.P., then the value of $x$ is

1. (A)$-2$
2. (B)2
3. (C)1
4. (D)$-1$

The $20^{\text{th}}$ term of an A.P, whose first term is $-2$ and the common difference is 4, is

1. (A)78
2. (B)74
3. (C)$-36$
4. (D)$-34$

If $p-1$, $p+1$ and $2p+3$ are in A.P., then the value of p is

1. (A)–2
2. (B)4
3. (C)0
4. (D)2

If a, b, c form an A.P. with common difference d, then the value of $a-2b-c$ is equal to

1. (A)2a + 4d
2. (B)0
3. (C)–2a – 4d
4. (D)–2a – 3d

The next term of the A.P. : $\sqrt{6}$, $\sqrt{24}$, $\sqrt{54}$ is :

1. (A)$\sqrt{60}$
2. (B)$\sqrt{96}$
3. (C)$\sqrt{72}$
4. (D)$\sqrt{216}$

Assertion (A) : a, b, c are in A.P. if and only if $2b=a+c$.
Reason (R) : The sum of first n odd natural numbers is $n^2$.

1. (A)Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
2. (B)Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation of Assertion (A).
3. (C)Assertion (A) is true but Reason (R) is false.
4. (D)Assertion (A) is false but Reason (R) is true.

If $k+2$, $4k-6$ and $3k-2$ are three consecutive terms of an A.P., then the value of k is :

1. (A)3
2. (B)$-3$
3. (C)4
4. (D)$-4$

The next term of the A.P. : $\sqrt{7}$, $\sqrt{28}$, $\sqrt{63}$ is :

1. (A)$\sqrt{70}$
2. (B)$\sqrt{80}$
3. (C)$\sqrt{97}$
4. (D)$\sqrt{112}$

The common difference of the A.P. whose $n^{th}$ term is given by $a_n=3n+7$, is :

1. (A)7
2. (B)3
3. (C)3n
4. (D)1

The $11^{th}$ term from the end of the A.P. : 10, 7, 4, ......., $-62$ is :

1. (A)25
2. (B)16
3. (C)$-32$
4. (D)0

The $13^{th}$ term from the end of the A.P. : 20, 13, 6, $-1$, ....., $-148$ is :

1. (A)57
2. (B)$-57$
3. (C)64
4. (D)$-64$

The common difference of the A.P. whose $n^{th}$ term is given by $a_n=5n-7$ is :

1. (A)$-7$
2. (B)7
3. (C)5
4. (D)$-2$

If the sum of the first n terms of an A.P be $3n^2+n$ and its common difference is 6, then its first term is

1. (A)2
2. (B)3
3. (C)1
4. (D)4