Which general term is correct for the sequence 5/2, 7, 27/2, 22, ...?
Answer and explanation
Correct answer: a_n = n(2n + 3)/2
The governing concept is finding an explicit formula for the nth term and verifying it with several initial positions. Test option A: for n = 1, it gives 1(2 + 3)/2 = 5/2; for n = 2, it gives 2(4 + 3)/2 = 7; for n = 3, it gives 3(6 + 3)/2 = 27/2; and for n = 4, it gives 4(8 + 3)/2 = 22. Thus it reproduces every displayed term, so A is correct. Option B gives 2 at n = 1, option C gives 3, and option D gives 2, so those alternatives fail immediately.
Frequently asked questions
What is the correct answer to this question?
a_n = n(2n + 3)/2
Why is this the correct answer?
The governing concept is finding an explicit formula for the nth term and verifying it with several initial positions. Test option A: for n = 1, it gives 1(2 + 3)/2 = 5/2; for n = 2, it gives 2(4 + 3)/2 = 7; for n = 3, it gives 3(6 + 3)/2 = 27/2; and for n = 4, it gives 4(8 + 3)/2 = 22. Thus it reproduces every displayed term, so A is correct. Option B gives 2 at n = 1, option C gives 3, and option D gives 2, so those alternatives fail immediately.
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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