What is the nth term of the sequence 5, 10, 15, 20, …?
Answer and explanation
Correct answer: aₙ = 5n
The key concept is recognizing a sequence whose terms are consecutive multiples of 5. The first term is 5, the second is 5 × 2, the third is 5 × 3, and the fourth is 5 × 4. Therefore the term in position n is 5 × n, or aₙ = 5n. Substitution verifies the rule: n = 1 gives 5, n = 2 gives 10, n = 3 gives 15, and n = 4 gives 20. Hence option B is correct. Option A gives 6 as the first term, option C gives 10 as the first term and grows twice as fast, and option D produces square numbers rather than the displayed multiples of 5. The rule must work for every position, not just one term.
Frequently asked questions
What is the correct answer to this question?
aₙ = 5n
Why is this the correct answer?
The key concept is recognizing a sequence whose terms are consecutive multiples of 5. The first term is 5, the second is 5 × 2, the third is 5 × 3, and the fourth is 5 × 4. Therefore the term in position n is 5 × n, or aₙ = 5n. Substitution verifies the rule: n = 1 gives 5, n = 2 gives 10, n = 3 gives 15, and n = 4 gives 20. Hence option B is correct. Option A gives 6 as the first term, option C gives 10 as the first term and grows twice as fast, and option D produces square numbers rather than the displayed multiples of 5. The rule must work for every position, not just one term.
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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