Which is (a_n) for the sequence (5,11,19,29,...)?
Answer and explanation
Correct answer: n²+2n+2
The governing concept is finding an explicit rule that produces the nth term of a sequence. Test option B at the known positions: when n=1, 1²+2(1)+2=5; when n=2, 2²+2(2)+2=10, which does not equal 11. Thus the supplied answer and option set contain an inconsistency: no listed option reproduces all four terms. In fact, the successive differences are 6, 8, and 10, so the second difference is 2. A quadratic rule has the form n²+bn+c; using the first terms gives b+c=4 and 2b+c=7, hence b=3 and c=1. The correct rule should be a_n=n²+3n+1, absent from the options. This item must be revised before being used.
Frequently asked questions
What is the correct answer to this question?
n²+2n+2
Why is this the correct answer?
The governing concept is finding an explicit rule that produces the nth term of a sequence. Test option B at the known positions: when n=1, 1²+2(1)+2=5; when n=2, 2²+2(2)+2=10, which does not equal 11. Thus the supplied answer and option set contain an inconsistency: no listed option reproduces all four terms. In fact, the successive differences are 6, 8, and 10, so the second difference is 2. A quadratic rule has the form n²+bn+c; using the first terms gives b+c=4 and 2b+c=7, hence b=3 and c=1. The correct rule should be a_n=n²+3n+1, absent from the options. This item must be revised before being used.
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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