What is the nth term of the sequence (3, 8, 13, 18, ...)?
Answer and explanation
Correct answer: aₙ = 5n − 2
The sequence is an arithmetic progression since every term increases by 5: 8 − 3 = 5, 13 − 8 = 5, and 18 − 13 = 5. The general term of an arithmetic progression is aₙ = a₁ + (n − 1)d. Here the first term is a₁ = 3 and the common difference is d = 5. Thus aₙ = 3 + (n − 1)5 = 3 + 5n − 5 = 5n − 2. Hence option A is correct. Substitution confirms the result: n = 1 gives 3, n = 2 gives 8, n = 3 gives 13, and n = 4 gives 18. Option B gives 7 as its first term; option C gives 8, and option D gives 6, so none of those can represent the given sequence.
Frequently asked questions
What is the correct answer to this question?
aₙ = 5n − 2
Why is this the correct answer?
The sequence is an arithmetic progression since every term increases by 5: 8 − 3 = 5, 13 − 8 = 5, and 18 − 13 = 5. The general term of an arithmetic progression is aₙ = a₁ + (n − 1)d. Here the first term is a₁ = 3 and the common difference is d = 5. Thus aₙ = 3 + (n − 1)5 = 3 + 5n − 5 = 5n − 2. Hence option A is correct. Substitution confirms the result: n = 1 gives 3, n = 2 gives 8, n = 3 gives 13, and n = 4 gives 18. Option B gives 7 as its first term; option C gives 8, and option D gives 6, so none of those can represent the given sequence.
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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