Chapter Exam

Chapter 6: Progressions — Online MCQ Test

Q: In an arithmetic progression, if the first term is 5 and common difference is 3, what is the 4th term?

Answer: A. 14 — Using the formula aₙ = a + (n-1)d, we get a₄ = 5 + (4-1)×3 = 5 + 9 = 14.

Q: Which of the following is NOT a characteristic of an arithmetic progression?

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.

Q: 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?

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.

Q: In an AP, if the sum of first n terms Sₙ = 3n² + 2n, which of the following is true about the AP?

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.

MATHS · CLASS 10th · Telangana State Board

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Chapter 6: Progressions — Important Questions & Answers (FAQ)

Frequently asked questions from Telangana State Board CLASS 10th MATHS — Chapter 6: Progressions, with answers and explanations. These are sample questions; the exam has its own separate question set.

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.

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.

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.

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.

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.