Arithmetic Progressions

What is the common difference of the AP: 3, 7, 11, 15, …?
a) 2
b) 3
c) 4
d) 5
Answer: c
Which term of the AP: 5, 10, 15, 20, … is 50?
a) 5
b) 6
c) 7
d) 10
Answer: b
Find the 10th term of the AP: 2, 4, 6, 8, …
a) 18
b) 20
c) 22
d) 24
Answer: b
The first term of an AP is 5, and the common difference is 2. What is the 15th term?
a) 30
b) 31
c) 33
d) 35
Answer: b
If the sum of the first n terms of an AP is
Sn=3n2+nS_n = 3n^2 + n
, find the first term.
a) 4
b) 3
c) 5
d) 6
Answer: a
Which of the following sequences is an AP?
a) 2, 4, 8, 16
b) 1, 4, 7, 10
c) 5, 10, 20, 40
d) 3, 9, 27, 81
Answer: b
If the common difference of an AP is negative, the sequence is:
a) Increasing
b) Decreasing
c) Constant
d) None of these
Answer: b
Find the sum of the first 5 terms of the AP: 1, 3, 5, 7, …
a) 15
b) 25
c) 35
d) 45
Answer: b
The nth term of an AP is given by
an=5n−3a_n = 5n – 3
. Find the 7th term.
a) 30
b) 32
c) 33
d) 34
Answer: d
How many terms are there in the AP: 3, 7, 11, …, 47?
a) 12
b) 11
c) 10
d) 13
Answer: a
Which term of the AP: 2, 5, 8, 11, … is 50?
a) 15
b) 16
c) 17
d) 18
Answer: c
What is the common difference of the AP where
a1=5a_1 = 5
and
a2=12a_2 = 12
?
a) 6
b) 7
c) 8
d) 9
Answer: b
The sum of the first 20 terms of the AP: 1, 4, 7, 10, … is:
a) 420
b) 440
c) 460
d) 480
Answer: a
What is the first term of an AP if its 5th term is 20 and the common difference is 3?
a) 8
b) 6
c) 5
d) 7
Answer: b
The common difference in the AP: 7, 13, 19, 25, … is:
a) 4
b) 5
c) 6
d) 7
Answer: c
If
an=3n+2a_n = 3n + 2
, find the 12th term.
a) 38
b) 36
c) 37
d) 39
Answer: c
In an AP,
a=6a = 6
,
d=−3d = -3
. Find
a5a_5
.
a) -3
b) 0
c) -6
d) -9
Answer: b
How many terms of the AP: 2, 4, 6, … will give a sum of 210?
a) 15
b) 14
c) 12
d) 16
Answer: a
Find the 25th term of the AP: 7, 13, 19, …
a) 151
b) 157
c) 161
d) 163
Answer: b
Which of the following is NOT an AP?
a) 2, 5, 8, 11
b) 3, 6, 12, 24
c) 10, 8, 6, 4
d) 5, 10, 15, 20
Answer: b
What is the sum of the first 10 terms of the AP: 3, 6, 9, …?
a) 120
b) 150
c) 180
d) 210
Answer: b
If the first term of an AP is 4 and the last term is 100, with a common difference of 4, how many terms are there?
a) 24
b) 25
c) 26
d) 23
Answer: b
The 15th term of an AP is 47, and the first term is 7. What is the common difference?
a) 2
b) 3
c) 4
d) 5
Answer: b
Find the 8th term of the AP: 5, 12, 19, …
a) 51
b) 52
c) 55
d) 56
Answer: a
In an AP, the sum of the first 20 terms is 400, and the first term is 7. What is the common difference?
a) 1
b) 2
c) 3
d) 4
Answer: c
If $S_n = n^2 + 2n$ is the sum of the first $n$ terms of an AP, what is its first term?
a) 2
b) 3
c) 1
d) 4
Answer: c
How many terms of the AP: 12, 15, 18, … are needed to make the sum 180?
a) 8
b) 9
c) 10
d) 11
Answer: b
The nth term of an AP is given as $a_n = 4n – 7$ . What is the 5th term?
a) 12
b) 13
c) 14
d) 15
Answer: b
In an AP, the 7th term is twice the 4th term, and the first term is 3. What is the common difference?
a) 1
b) 2
c) 3
d) 4
Answer: c
The sum of the first 12 terms of an AP is 156, and the common difference is 2. Find the first term.
a) 7
b) 5
c) 6
d) 4
Answer: d
Which of the following sequences is an AP?
a) 10, 15, 21, 28
b) 7, 7, 7, 7
c) 1, 4, 9, 16
d) 2, 3, 5, 8
Answer: b
The 10th term of an AP is 50, and the first term is 5. What is the common difference?
a) 4
b) 5
c) 6
d) 7
Answer: b
If the first term of an AP is 2 and the last term is 50 with a common difference of 6, find the number of terms.
a) 8
b) 9
c) 10
d) 11
Answer: d
Find the sum of the AP: 10, 20, 30, …, up to 12 terms.
a) 720
b) 650
c) 780
d) 840
Answer: a
The nth term of an AP is $7 n - 3$ . What is the first term?
a) 3
b) 4
c) 7
d) 5
Answer: b
In an AP, $a = 10$ and $d = - 3$ . What is the 5th term?
a) -2
b) -3
c) 1
d) -5
Answer: c
The sum of the first 8 terms of the AP: 3, 6, 9, … is:
a) 108
b) 112
c) 96
d) 124
Answer: a
The 20th term of an AP is 45, and the first term is 5. What is the common difference?
a) 2
b) 2.5
c) 3
d) 4
Answer: c
In an AP: $a = 8$ , $S_{10} = 80$ , find the common difference.
a) 1
b) 2
c) 3
d) 4
Answer: a
How many terms are there in the AP: 5, 10, 15, …, 100?
a) 18
b) 19
c) 20
d) 21
Answer: b
Find the sum of the AP: 8, 16, 24, …, up to 15 terms.
a) 960
b) 1040
c) 960
d) 1000
Answer: c
If the 4th term of an AP is 20 and the common difference is 5, what is the first term?
a) 5
b) 6
c) 8
d) 10
Answer: d
The nth term of an AP is $2 n + 3$ . What is the sum of the first 10 terms?
a) 80
b) 100
c) 120
d) 140
Answer: d
The first and last terms of an AP are 2 and 20, respectively, and the common difference is 3. Find the sum of all terms.
a) 120
b) 110
c) 130
d) 150
Answer: a
Find the 15th term of the AP: 6, 9, 12, …
a) 45
b) 48
c) 51
d) 54
Answer: c
The sum of the first 25 terms of the AP: 2, 4, 6, … is:
a) 625
b) 650
c) 675
d) 700
Answer: a
If , , and , find the 20th term.
a) 65
b) 60
c) 62
d) 70
Answer: b
Find the sum of the first 50 terms of the AP: 10, 15, 20, …
a) 3650
b) 3750
c) 3850
d) 3950
Answer: b
The common difference of the AP: 4, 9, 14, 19, … is:
a) 5
b) 6
c) 4
d) 3
Answer: a
How many terms are required for the sum of the AP: 7, 10, 13, … to be 148?
a) 8
b) 9
c) 10
d) 11
Answer: