Which is the nth term of the sequence 6, 11, 16, 21, …?
Answer and explanation
Correct answer: aₙ = 5n + 1
The sequence is arithmetic because each term increases by the constant difference 5. With first term a₁ = 6 and common difference d = 5, the nth-term formula is aₙ = a₁ + (n − 1)d. Substitution gives aₙ = 6 + 5(n − 1) = 6 + 5n − 5 = 5n + 1. Therefore option A is correct. Verification is important: n = 1 gives 5(1) + 1 = 6, n = 2 gives 11, and n = 4 gives 21. Option B gives 5 when n = 1, option C gives 4, and option D has a common difference of only 1. These checks show why the selected expression is the only one matching all displayed terms.
Frequently asked questions
What is the correct answer to this question?
aₙ = 5n + 1
Why is this the correct answer?
The sequence is arithmetic because each term increases by the constant difference 5. With first term a₁ = 6 and common difference d = 5, the nth-term formula is aₙ = a₁ + (n − 1)d. Substitution gives aₙ = 6 + 5(n − 1) = 6 + 5n − 5 = 5n + 1. Therefore option A is correct. Verification is important: n = 1 gives 5(1) + 1 = 6, n = 2 gives 11, and n = 4 gives 21. Option B gives 5 when n = 1, option C gives 4, and option D has a common difference of only 1. These checks show why the selected expression is the only one matching all displayed terms.
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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