If (p,,p+7,,p+14,\ldots) is an arithmetic progression, what is the common difference?
Correct answer: B
The difference between the second and first terms is ((p+7)-p=7). In exams, subtract even with algebraic terms.
View question detailsMathematics
Arithmetic Progression
समांतर श्रेणी
Arithmetic Progression for Class 9 Mathematics introduces a sequence in which consecutive terms change by a constant common difference. Students learn to recognise the pattern, identify the first term and common difference, generate further terms, and use the nth-term rule to find a required term. As part of Sequences and Progressions, the topic builds clear reasoning through number patterns, tables, and simple problems, helping learners connect a general rule with specific values and explain their steps accurately.
TOPIC PRACTICE
Quiz this set
Up to 20 questions from this page. Select your focus, then start.
20 questions
Choose questions
Easy · Level 55 · sequences,progressions,arithmetic-progression,class-9,easy,Arithmetic Progression,Sequences and Progressions,Mathematics
View options
- (p)
- (7)
- (14)
- (21)
Easy · Level 55 · sequences,progressions,arithmetic-progression,class-9,easy
View options
- (0)
- (1)
- (11)
- (-11)
Easy · Level 55 · sequences,progressions,arithmetic-progression,class-9,easy,Arithmetic Progression,Sequences and Progressions,Mathematics
View options
- (15,0,15)
- (0,15,30)
- (15,15,15)
- (15,30,45)
Easy · Level 55 · sequences,progressions,arithmetic-progression,class-9,easy
View options
- (9)
- (10)
- (11)
- (12)
Easy · Level 55 · sequences,progressions,arithmetic-progression,class-9,easy
View options
- (2)
- (7)
- (9)
- (11)
Easy · Level 55 · arithmetic progression, nth term, common difference, sequences, class 9 mathematics
View options
- 38
- 40
- 43
- 45
Easy · Level 55 · arithmetic progression, nth term, common difference, sequences, class 9 mathematics
View options
- \(31\)
- \(36\)
- \(40\)
- \(43\)
Easy · Level 55 · arithmetic progression, sequences, common difference, classification, class 9 mathematics
View options
- Arithmetic progression
- Geometric progression
- Harmonic progression
- Fibonacci sequence
Easy · Level 55 · sequences,progressions,arithmetic-progression,class-9,easy
View options
- (99)
- (110)
- (121)
- (132)
Easy · Level 55 · arithmetic progression,sequences and progressions,nth term,class 9 mathematics,substitution
View options
- 4
- 5
- 6
- 8
Easy · Level 55 · sequences,progressions,arithmetic-progression,class-9,easy
View options
- (a_n=14-4n)
- (a_n=18-4n)
- (a_n=4n+10)
- (a_n=14+n)
Easy · Level 55 · sequences,progressions,arithmetic-progression,class-9,easy
View options
- (18)
- (20)
- (21)
- (24)
Easy · Level 55 · arithmetic progression,sequences and progressions,nth term,common difference,class 9 mathematics
View options
- 70
- 72
- 76
- 78
Easy · Level 55 · sequences,progressions,arithmetic-progression,class-9,easy,Arithmetic Progression,Sequences and Progressions,Mathematics
View options
- (12,18,24,30,\ldots)
- (6,12,18,24,\ldots)
- (12,24,36,48,\ldots)
- (18,24,30,36,\ldots)
Easy · Level 55 · arithmetic progression, nth term, common difference, sequences, class 9 mathematics
View options
- 38
- 42
- 45
- 47
Medium · Level 52 · arithmetic_progression,common_difference,sequences,constant_difference,nth_term,Arithmetic Progression,Sequences and Progressions,Mathematics
View options
- 5
- 6
- 7
- 13
Medium · Level 52 · arithmetic progression, common difference, sequence, misconception, class 9 mathematics
View options
- The differences between consecutive terms are not equal
- The first term is not positive
- The number of terms is not even
- All terms of the sequence are not integers
Medium · Level 52 · sequences,progressions,arithmetic-progression,general-term
View options
- (a_n=48-6n)
- (a_n=42-6n)
- (a_n=6n+36)
- (a_n=48+6n)
Medium · Level 52 · arithmetic progression, common difference, sequence analysis, misconception, class 9 mathematics
View options
- The consecutive differences 3, 4, 5 are not equal.
- All terms of an arithmetic progression cannot be positive.
- The first term of an arithmetic progression cannot be 2.
- Terms of an arithmetic progression cannot increase.
Medium · Level 52 · sequences,progressions,arithmetic-progression,term-position
View options
- (7)th
- (8)th
- (9)th
- (10)th
What is the common difference in the arithmetic progression (11,11,11,11,\ldots)?
Correct answer: A
Consecutive terms are equal, so the difference is (11-11=0). In exams, a constant sequence can also be an arithmetic progression.
View question detailsIf (a=15) and (d=0), what are the first three terms?
Correct answer: C
When the common difference is (0), all terms remain (15). In exams, (d=0) means a constant sequence.
View question detailsWhat is the missing term in the arithmetic progression (4,\Box,18,25,\ldots)?
Correct answer: C
The difference between (18) and (25) is (7), so the missing term is (18-7=11). In exams, apply the common difference backward too.
View question detailsIf (a_n=9n-2), what is the common difference of this arithmetic progression?
Correct answer: C
In the linear rule (a_n=9n-2), the coefficient of (n) is the difference (9). In exams, take (k) as (d) in (kn+c).
View question detailsWhat is (a_6) of the arithmetic progression (18,23,28,33,\ldots)?
Correct answer: C
The first term is 18 and the common difference is 5. Therefore, the sixth term is \(a_6=a+(6-1)d=18+5\times5=43\). Choosing 40 results from adding the common difference only four times. Exam tip: use \(a_n=a+(n-1)d\) for the nth term of an AP.
View question detailsIf an arithmetic progression has (a_1=13) and (d=9), what is (a_4)?
Correct answer: C
The nth term of an arithmetic progression is \(a_n=a_1+(n-1)d\). Therefore, \(a_4=13+(4-1)\times 9=13+27=40\). Hence, \(40\) is correct. \(43\) would result from adding the common difference four times, but only three differences are added to reach the fourth term. Exam tip: use \(n-1\), not \(n\), when finding \(a_n\).
View question detailsWhat is a sequence called in which the difference between each term and the term immediately preceding it remains constant?
Correct answer: A
In an arithmetic progression, the difference between consecutive terms, called the common difference, is constant; for example, 3, 8, 13 has difference 5. A geometric progression has a constant ratio, not a constant difference. Exam tip: “constant difference” identifies an AP.
View question detailsWhat is the tenth term of the arithmetic progression (11,22,33,44,\ldots)?
Correct answer: B
This is a sequence of multiples of (11), so the tenth term is (110). In exams, identify multiples quickly.
View question detailsIf (a_n=18-4n), what is the value of (a_3)?
Correct answer: C
Given \(a_n=18-4n\), substitute \(n=3\): \(a_3=18-4(3)=18-12=6\). Hence, 6 is the correct option. A value such as 8 can result from an incorrect calculation of \(4\times3\). Exam tip: while finding a term, substitute the value of \(n\) carefully into the complete expression.
View question detailsWhat is the general term of the arithmetic progression (14,10,6,2,\ldots)?
Correct answer: B
At (n=1) it gives (14), and at (n=2) it gives (10), so (a_n=18-4n). In exams, choose the rule after checking the first term.
View question detailsIf (12,,x,,30) is an arithmetic progression, what is the value of (x)?
Correct answer: C
The middle term is the average of (12) and (30), so (x=\frac{12+30}{2}=21). In exams, take the average for the middle term in three-term progressions.
View question detailsWhat will be the seventh term in the arithmetic progression (30,38,46,54,\ldots)?
Correct answer: D
Here, the first term is \(a=30\) and the common difference is \(d=38-30=8\). The \(n\)th term is \(a_n=a+(n-1)d\). Therefore, \(a_7=30+(7-1)\times 8=30+48=78\). Option 76 would result from adding the difference only five times, but the seventh term requires six additions of the common difference. Exam tip: always use \(n-1\) in the formula for the \(n\)th term.
View question detailsWhich arithmetic progression has first term (12) and common difference (6)?
Correct answer: A
The first term is (12), and (6) is added each time. In exams, match both the first term and the difference.
View question detailsIf (a=10) and (d=7), what will be the sixth term of the arithmetic progression?
Correct answer: C
The nth term of an arithmetic progression is \(a_n=a+(n-1)d\). Therefore, \(a_6=10+(6-1)\times7=10+35=45\). The value 42 is obtained by adding the common difference only four times, so it is the fifth term. Exam tip: always subtract 1 from the term number before multiplying by \(d\).
View question detailsWhat is the common difference in the sequence (6, 13, 20, 27, …)?
Correct answer: C
The governing concept is the common difference of an arithmetic progression. It is the constant amount found by subtracting one term from the next. Compute the differences: 13 − 6 = 7, 20 − 13 = 7, and 27 − 20 = 7. Because all checked consecutive differences are equal, the sequence follows an arithmetic pattern and its common difference is 7. Therefore, option C is correct. Option D, 13, is the second term rather than the change between terms. Options A and B do not equal the difference between any consecutive pair in the sequence. Checking several pairs is important because it confirms that 7 is a constant difference, not merely a result from one isolated subtraction.
View question detailsRiya says that the sequence 3, 7, 11, 16 is an arithmetic progression because its terms are increasing. What is the error in Riya's reasoning?
Correct answer: A
In an AP, the difference between every pair of consecutive terms must be the same. Here \(7-3=4\), \(11-7=4\), but \(16-11=5\). Increasing terms alone do not make an AP. Exam tip: check consecutive differences first.
View question detailsWhat is the (n)th term of the arithmetic progression (42,36,30,24,\ldots)?
Correct answer: A
The first term is (42) and the difference is (-6), so (a_n=42+(n-1)(-6)=48-6n). In a decreasing progression, the common difference is negative.
View question detailsA student says that the sequence 2, 5, 9, 14 is an arithmetic progression because its terms are continuously increasing. What is the student's error?
Correct answer: A
In an arithmetic progression, the difference between consecutive terms must be constant. Here, 5−2=3, 9−5=4 and 14−9=5, which are unequal. Increasing terms alone do not form an AP. In exams, check consecutive differences first.
View question detailsIn the arithmetic progression (3,11,19,27,\ldots), which term is (67)?
Correct answer: C
From (3+(n-1)8=67), (8(n-1)=64) and (n=9). To find the position, set the given term equal to (a_n).
View question detailsQUIZ COMPLETE