Kerala SSLC · Mathematics · Class 10

Arithmetic Sequences: Important Questions with Answers

These are 10 important multiple-choice questions from the Kerala SSLC Mathematics chapter “Arithmetic Sequences” (Kerala SCERT syllabus). Each one shows the correct answer and a short explanation of why it is right. Try answering before you read the answer. ExamSummary has 49 practice questions on this chapter in total.

1. Q1.Which of the following sequences is an Arithmetic Progression (AP)?

   • A)2, 4, 8, 16
   • B)1, 4, 9, 16
   • C)3, 7, 11, 15
   • D)1, 2, 4, 8

   Answer: C) 3, 7, 11, 15

   In an Arithmetic Progression, the difference between consecutive terms must be constant. Here, 7-3=4, 11-7=4, and 15-11=4, making the common difference uniform.

2. Q2.What is the fundamental condition required for a sequence of numbers to be classified as an Arithmetic Progression?

   • A)The difference between consecutive terms must be constant.
   • B)The ratio between consecutive terms must be constant.
   • C)The sum of consecutive terms must be increasing.
   • D)Every alternate term must be greater than the previous one.

   Answer: A) The difference between consecutive terms must be constant.

   In an Arithmetic Progression, the difference between any two consecutive terms is always a fixed value called the common difference. This constant difference defines the progression regardless of whether the terms are increasing or decreasing.

3. Q3.Find the 15th term of the arithmetic progression: 5, 8, 11, ...

   • A)45
   • B)47
   • C)49
   • D)51

   Answer: B) 47

   Use the formula for the nth term, a_n = a + (n-1)d. Substituting a=5, d=3, and n=15 gives 5 + 14(3) = 47.

4. Q4.If the 3rd term of an AP is 10 and the 7th term is 22, what is the common difference?

   • A)2
   • B)3
   • C)4
   • D)5

   Answer: B) 3

   The difference between the 7th and 3rd terms corresponds to 4 times the common difference. Solving 22 - 10 = 4d yields d = 3.

5. Q5.What is the sum of the first 50 even natural numbers?

   • A)2450
   • B)2500
   • C)2550
   • D)2600

   Answer: C) 2550

   The sum of the first n even numbers is calculated using the formula n(n+1). For n=50, the sum is 50 multiplied by 51, which equals 2550.

6. Q6.Which condition must be satisfied for three numbers x, y, and z to be in Arithmetic Progression?

   • A)x + z = y
   • B)2y = x + z
   • C)y^2 = xz
   • D)x + y + z = 0

   Answer: B) 2y = x + z

   In an AP, the middle term is the arithmetic mean of the adjacent terms. Therefore, the difference between consecutive terms must be equal, resulting in 2y = x + z.

7. Q7.How many terms are there in the sequence 7, 11, 15, ..., 127?

   • A)30
   • B)31
   • C)32
   • D)33

   Answer: B) 31

   Using the last term formula l = a + (n-1)d, we substitute 127 = 7 + (n-1)4. Simplifying this equation gives 120 = 4(n-1), leading to n = 31.

8. Q8.Find the middle term of the arithmetic progression: 2, 5, 8, ..., 50.

   • A)24
   • B)26
   • C)28
   • D)30

   Answer: B) 26

   First, calculate the total number of terms which is 17. The middle term is the 9th term, found by calculating 2 + (9-1)3, which equals 26.

9. Q9.A person saves Rs. 50 in the first month and increases savings by Rs. 20 every month. How much is saved in the 10th month?

   • A)200
   • B)210
   • C)230
   • D)250

   Answer: C) 230

   This forms an AP where the first term is 50 and the common difference is 20. The 10th term is calculated as 50 + 9(20), which equals 230.

10. Q10.For what value of k will the terms k, 2k-1, and 2k+7 be consecutive terms of an AP?

    • A)7
    • B)8
    • C)9
    • D)10

    Answer: C) 9

    Set the difference between consecutive terms equal: (2k-1) - k = (2k+7) - (2k-1). This simplifies to k-1 = 8, giving the solution k = 9.

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