Class 10 Arithmetic Progressions Mock Test (CBSE)

Topics in Arithmetic Progressions

• Arithmetic progressions
• nth term of an AP
• Sum of first n terms of an AP

Arithmetic Progressions practice questions with answers

1. Q1Multiple choice·1 mark
   If the sum of the first $p$ terms of an arithmetic progression is equal to the sum of its first $q$ terms (where $p \neq q$), then the sum of the first $(p+q)$ terms is:

   1. (a)$p + q$
   2. (b)$-(p + q)$
   3. (c)$0$
   4. (d)$1$
   Show answer and step marks

   1. Correct option: (c) $0$. Using $S_p = S_q$, we derive $2a + (p+q-1)d = 0$, leading to $S_{p+q} = \frac{p+q}{2} \times 0 = 0$.+1

   Answer: (c)
2. Q2Multiple choice·1 mark
   If the sum of the first $n$ terms of an AP is given by $S_n = 3n^2 + n$, then its 2nd term is:

   1. (a)$7$
   2. (b)$10$
   3. (c)$4$
   4. (d)$14$
   Show answer and step marks

   1. Correct option: (b) $10$. Using $a_2 = S_2 - S_1$, where $S_1 = 3(1)^2 + 1 = 4$ and $S_2 = 3(2)^2 + 2 = 14$, we get $a_2 = 14 - 4 = 10$, which corresponds to option (b).+1

   Answer: (b)
3. Q3Assertion and reason·1 mark
   Assertion (A): The sequence $1, 4, 9, 16, \dots$ is an arithmetic progression. Reason (R): The differences between consecutive terms are $3, 5, 7, \dots$, which are not equal.

   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.
   Show answer and step marks

   1. Correct option: (d) Assertion (A) is false but Reason (R) is true.+1

   Answer: (d)
4. Q4Assertion and reason·1 mark
   Assertion (A): The 11th term of the AP $-5, -\frac{5}{2}, 0, \frac{5}{2}, \dots$ is $20$. Reason (R): The $n^{\text{th}}$ term of an AP is given by $a_n = a + (n-1)d$.

   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 Assertion (A).
   3. (c)Assertion (A) is true but Reason (R) is false.
   4. (d)Assertion (A) is false but Reason (R) is true.
   Show answer and step marks

   1. Correct option: (a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A). For the given AP, $a = -5$ and $d = \frac{5}{2}$. Using $a_{11} = -5 + (11-1)\left(\frac{5}{2}\right) = 20$, Assertion is true. Reason correctly states the formula for the $n^{\text{th}}$ term and explains the Assertion.+1

   Answer: (a)
5. Q5Short answer·2 marks
   Decide whether the list of numbers $7, 11, 15, 20, 23, \dots$ is an arithmetic progression (AP). Give a reason based on the differences between consecutive terms.
   Show answer and step marks

   1. Find the differences of consecutive terms: $11-7=4$, $15-11=4$, $20-15=5$, $23-20=3$.+1
   2. The differences are not the same, so the list is not an AP. Final answer: Not an AP.+1

   Answer: Not an AP, because the differences $4, 4, 5, 3$ are not equal.
6. Q6Short answer·2 marks
   A museum arranges its display stands in rows. The first row has $4$ stands, and every row after the first has $3$ more stands than the row just before it. In which row does the number of stands become more than $40$ for the first time?
   Show answer and step marks

   1. The numbers of stands form an AP with $a = 4$, $d = 3$, so the $n$th row has $a_n = 4 + (n-1)\times 3$ stands+1
   2. Require $4 + 3(n-1) > 40$, so $3(n-1) > 36$ and $n - 1 > 12$, giving $n > 13$+0.5
   3. The smallest whole number is $n = 14$; row 14 has $4 + 39 = 43$ stands+0.5

   Answer: Row 14 (it has 43 stands)

More Class 10 Maths mock tests