The first four terms of an arithmetic sequence are 7, 11, 15, 19. What is its nth term?
Answer and explanation
Correct answer: 4n + 3
The governing concept is the general term of an arithmetic sequence. The consecutive differences are 11−7 = 4, 15−11 = 4, and 19−15 = 4, so the common difference is d = 4 and the first term is a₁ = 7. Applying aₙ = a₁ + (n−1)d gives aₙ = 7 + (n−1)4 = 7 + 4n − 4 = 4n + 3. Therefore option A is correct. Substitution verifies the rule: n = 1 gives 7, n = 2 gives 11, n = 3 gives 15, and n = 4 gives 19. Option B has an incorrect coefficient and constant; options C and D also fail to reproduce the stated first term and the constant difference.
Frequently asked questions
What is the correct answer to this question?
4n + 3
Why is this the correct answer?
The governing concept is the general term of an arithmetic sequence. The consecutive differences are 11−7 = 4, 15−11 = 4, and 19−15 = 4, so the common difference is d = 4 and the first term is a₁ = 7. Applying aₙ = a₁ + (n−1)d gives aₙ = 7 + (n−1)4 = 7 + 4n − 4 = 4n + 3. Therefore option A is correct. Substitution verifies the rule: n = 1 gives 7, n = 2 gives 11, n = 3 gives 15, and n = 4 gives 19. Option B has an incorrect coefficient and constant; options C and D also fail to reproduce the stated first term and the constant difference.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Sequences and Progressions. Topic: nth term.
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