Which is the nth term of the sequence 1, 4, 10, 20, 35, …?
Answer and explanation
Correct answer: n(n + 1)(n + 2)/6
The governing concept is recognizing the formula for tetrahedral numbers, or cumulative sums of triangular numbers. The proposed rule in option B gives n = 1: 1·2·3/6 = 1; n = 2: 2·3·4/6 = 4; n = 3: 3·4·5/6 = 10; n = 4: 4·5·6/6 = 20; and n = 5: 5·6·7/6 = 35. Thus it matches every displayed term. The first differences are 3, 6, 10, 15, which are triangular numbers, supporting the same conclusion. Option A is only the triangular-number formula, while options C and D fail when checked against later terms.
Frequently asked questions
What is the correct answer to this question?
n(n + 1)(n + 2)/6
Why is this the correct answer?
The governing concept is recognizing the formula for tetrahedral numbers, or cumulative sums of triangular numbers. The proposed rule in option B gives n = 1: 1·2·3/6 = 1; n = 2: 2·3·4/6 = 4; n = 3: 3·4·5/6 = 10; n = 4: 4·5·6/6 = 20; and n = 5: 5·6·7/6 = 35. Thus it matches every displayed term. The first differences are 3, 6, 10, 15, which are triangular numbers, supporting the same conclusion. Option A is only the triangular-number formula, while options C and D fail when checked against later 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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