Chapter 6: Progressions — Online MCQ Test
MATHS · CLASS 10th · Telangana State Board
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This chapter covers: This chapter introduces numerical sequences.
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Chapter 6: Progressions — Important Questions & Answers
What is a sequence?
- A. An ordered list of numbers following a specific pattern or rule
- B. A random collection of numbers
- C. A set of numbers without any order
- D. A mathematical equation
Answer: A. An ordered list of numbers following a specific pattern or rule
A sequence is a systematic arrangement of numbers in a definite order, where each term follows a specific pattern or rule established by a mathematical formula.
A sequence is a systematic arrangement of numbers in a definite order, where each term follows a specific pattern or rule established by a mathematical formula.
In an arithmetic progression, if the first term is 5 and common difference is 3, what is the 4th term?
- A. 14
- B. 17
- C. 11
- D. 20
Answer: A. 14
Using the formula aₙ = a + (n-1)d, we get a₄ = 5 + (4-1)×3 = 5 + 9 = 14.
Using the formula aₙ = a + (n-1)d, we get a₄ = 5 + (4-1)×3 = 5 + 9 = 14.
Which of the following is NOT a characteristic of an arithmetic progression?
- A. Constant difference between consecutive terms
- B. Linear pattern of growth
- C. Constant ratio between consecutive terms
- D. Can be represented by aₙ = a + (n-1)d
Answer: C. Constant ratio between consecutive terms
A constant ratio between consecutive terms is the characteristic of a geometric progression, not an arithmetic progression. AP is defined by constant differences, not ratios.
A constant ratio between consecutive terms is the characteristic of a geometric progression, not an arithmetic progression. AP is defined by constant differences, not ratios.
The sum of an infinite geometric series with |r| < 1 is given by S = a/(1-r). If a = 8 and r = 1/2, what is S?
- A. 16
- B. 8
- C. 12
- D. 4
Answer: A. 16
Using S = a/(1-r), we get S = 8/(1-1/2) = 8/(1/2) = 16. This formula applies when the common ratio has absolute value less than 1.
Using S = a/(1-r), we get S = 8/(1-1/2) = 8/(1/2) = 16. This formula applies when the common ratio has absolute value less than 1.
In an AP, if the sum of first n terms Sₙ = 3n² + 2n, which of the following is true about the AP?
- A. First term is 5 and common difference is 6
- B. First term is 5 and common difference is 5
- C. First term is 3 and common difference is 6
- D. First term is 3 and common difference is 3
Answer: A. First term is 5 and common difference is 6
First term a₁ = S₁ = 3(1)² + 2(1) = 5. Second term a₂ = S₂ - S₁ = 3(4) + 2(2) - 5 = 16 - 5 = 11. Therefore, d = 11 - 5 = 6.
First term a₁ = S₁ = 3(1)² + 2(1) = 5. Second term a₂ = S₂ - S₁ = 3(4) + 2(2) - 5 = 16 - 5 = 11. Therefore, d = 11 - 5 = 6.