What is the general term of the sequence 7/3, 6, 11, 52/3, ...?
Answer and explanation
Correct answer: a_n = (2n^2 + 5n)/3
The governing concept is obtaining an nth-term formula and checking it at each given index, including fractional values. For option A, n = 1 gives (2 + 5)/3 = 7/3; n = 2 gives (8 + 10)/3 = 6; n = 3 gives (18 + 15)/3 = 11; and n = 4 gives (32 + 20)/3 = 52/3. Thus A reproduces the sequence exactly. Option B gives 1, 3, 6, 10, while option C gives 3, 5, 7, 9. Option D gives 2, 13/2, 14, 25/2, so neither matches the listed terms.
Frequently asked questions
What is the correct answer to this question?
a_n = (2n^2 + 5n)/3
Why is this the correct answer?
The governing concept is obtaining an nth-term formula and checking it at each given index, including fractional values. For option A, n = 1 gives (2 + 5)/3 = 7/3; n = 2 gives (8 + 10)/3 = 6; n = 3 gives (18 + 15)/3 = 11; and n = 4 gives (32 + 20)/3 = 52/3. Thus A reproduces the sequence exactly. Option B gives 1, 3, 6, 10, while option C gives 3, 5, 7, 9. Option D gives 2, 13/2, 14, 25/2, so neither matches the listed 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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