What is the general term of the sequence (1, 3, 6, 10, …)?
Answer and explanation
Correct answer: a_n = n(n + 1)/2
These are triangular numbers: 1 = 1·2/2, 3 = 2·3/2, 6 = 3·4/2, and 10 = 4·5/2. The nth triangular number is therefore a_n = n(n + 1)/2, so option C is correct. The successive differences are 2, 3, and 4, which also show why a simple arithmetic formula with a constant difference is not appropriate. Substitution gives the listed values for n = 1, 2, 3, and 4. Option A gives 1, 4, 9, 16; option B gives 1, 3, 5, 7; and option D gives 3, 4, 5, 6. Thus the triangular-number formula is the only option that reproduces the complete sequence.
Frequently asked questions
What is the correct answer to this question?
a_n = n(n + 1)/2
Why is this the correct answer?
These are triangular numbers: 1 = 1·2/2, 3 = 2·3/2, 6 = 3·4/2, and 10 = 4·5/2. The nth triangular number is therefore a_n = n(n + 1)/2, so option C is correct. The successive differences are 2, 3, and 4, which also show why a simple arithmetic formula with a constant difference is not appropriate. Substitution gives the listed values for n = 1, 2, 3, and 4. Option A gives 1, 4, 9, 16; option B gives 1, 3, 5, 7; and option D gives 3, 4, 5, 6. Thus the triangular-number formula is the only option that reproduces the complete sequence.
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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