Arithmetic Progressions (10 Mathematics)
An arithmetic progression is a sequence where consecutive terms have a constant difference. Understanding APs helps solve problems involving sequences and
TL;DR: An arithmetic progression is a sequence where consecutive terms have a constant difference. Understanding APs helps solve problems involving sequences…
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An arithmetic progression is a sequence where consecutive terms have a constant difference. Understanding APs helps solve problems involving sequences and
Arithmetic Progressions MCQs with Answers & Explanations
Q1. What is the common difference in the sequence 3, 7, 11, 15, ...?
- 3
- 4 ✓ (correct)
- 7
- 11
Q2. What is the nth term of an AP given by the formula?
- an = a1 + (n-1)d ✓ (correct)
- an = a1 + nd
- an = a1 + n
- an = a1 * n
Q3. What is the 5th term of AP: 2, 5, 8, 11, ...?
- 14 ✓ (correct)
- 15
- 16
- 17
Q4. What is the sum of first n terms of an AP?
- Sn = n/2 * (2a1 + (n-1)d) ✓ (correct)
- Sn = n * a1
- Sn = n * d
- Sn = (a1 + an)
Q5. How many terms are there in AP: 2, 5, 8, ..., 29?
- 8
- 9 ✓ (correct)
- 10
- 11
Q6. What is the sum of first 10 natural numbers?
- 45
- 55 ✓ (correct)
- 50
- 60
Q7. If a1 = 5 and d = 2, what is a3?
- 7
- 8
- 9 ✓ (correct)
- 10
Q8. Is 0 part of the AP: -5, -3, -1, 1, 3, ...?
- Yes, it is the 4th term ✓ (correct)
- No, 0 is not in this sequence
- Yes, it is the 3rd term
- Cannot be determined
Q9. What is the arithmetic mean of 5 and 15?
- 10 ✓ (correct)
- 8
- 12
- 20
Q10. If the sum of first n terms is 2n^2 + n, what is d?
- 1
- 2
- 3 ✓ (correct)
- 4
Frequently Asked Questions
What is the difference between an AP and a GP?
In an AP (Arithmetic Progression), consecutive terms have a constant difference (d). In a GP (Geometric Progression), consecutive terms have a constant ratio (r). APs have linear growth while GPs have exponential growth.
Can an AP have a common difference of 0?
Yes, when d = 0, all terms are equal. For example, 5, 5, 5, 5, ... is an AP with d = 0. This is called a constant sequence.
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