Which explicit rule is correct for the sequence (5,10,17,28,\ldots)?
Answer and explanation
Correct answer: (a_n=2^n+3n)
An explicit rule should produce every listed term when the position n is replaced by 1, 2, 3, and so on. The first term is obtained with n=1, the second with n=2, and the fourth with n=4. Testing several terms is important because a rule may match one value by coincidence. Here option A combines an exponential part \\(2^n\\) with a linear part \\(3n\\).
For option A, at n=1 we get \\(2^1+3(1)=5\\); at n=2, \\(2^2+3(2)=10\\); at n=3, \\(2^3+3(3)=17\\); and at n=4, \\(2^4+3(4)=28\\). These are exactly the given terms, so option A is correct. The other rules fail at one or more early positions and therefore cannot be the stated explicit rule.
Frequently asked questions
What is the correct answer to this question?
(a_n=2^n+3n)
Why is this the correct answer?
An explicit rule should produce every listed term when the position n is replaced by 1, 2, 3, and so on. The first term is obtained with n=1, the second with n=2, and the fourth with n=4. Testing several terms is important because a rule may match one value by coincidence. Here option A combines an exponential part \\(2^n\\) with a linear part \\(3n\\).
For option A, at n=1 we get \\(2^1+3(1)=5\\); at n=2, \\(2^2+3(2)=10\\); at n=3, \\(2^3+3(3)=17\\); and at n=4, \\(2^4+3(4)=28\\). These are exactly the given terms, so option A is correct. The other rules fail at one or more early positions and therefore cannot be the stated explicit rule.
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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