What is the general term of the sequence (10, 20, 30, 40, …)?
Answer and explanation
Correct answer: a_n = 10n
This question tests recognition of an explicit rule. Every displayed term is obtained by multiplying its position number by 10: the first term is 10 × 1, the second is 10 × 2, the third is 10 × 3, and the fourth is 10 × 4. Therefore the general term is a_n = 10n, so option C is correct. It can also be verified using the arithmetic-sequence formula: a_1 = 10 and d = 10, hence a_n = 10 + (n − 1)10 = 10n. Option A gives 11 as its second term, option B gives 5, 10, 15, …, and option D gives 9 for n = 1. Thus none of those alternatives reproduces all the listed terms.
Frequently asked questions
What is the correct answer to this question?
a_n = 10n
Why is this the correct answer?
This question tests recognition of an explicit rule. Every displayed term is obtained by multiplying its position number by 10: the first term is 10 × 1, the second is 10 × 2, the third is 10 × 3, and the fourth is 10 × 4. Therefore the general term is a_n = 10n, so option C is correct. It can also be verified using the arithmetic-sequence formula: a_1 = 10 and d = 10, hence a_n = 10 + (n − 1)10 = 10n. Option A gives 11 as its second term, option B gives 5, 10, 15, …, and option D gives 9 for n = 1. Thus none of those alternatives reproduces all the listed terms.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Sequences and Progressions. Topic: Explicit or general rule.
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