What is the general term of the sequence (7,22,47,82,\ldots)?
Answer and explanation
Correct answer: (a_n=5n^2+2)
The terms do not have a constant first difference: the differences are 15, 25, and 35. However, these differences increase by 10, suggesting a quadratic rule. The proposed expression \(5n^2+2\) can be checked directly by substituting the small positive indices. Testing the first few positions is an efficient way to verify a general term when answer choices are provided.
For \(n=1\), \(5(1)^2+2=7\); for \(n=2\), \(5(2)^2+2=22\); for \(n=3\), it gives 47; and for \(n=4\), it gives 82. Thus it reproduces every displayed term, so option A is correct. The linear choices cannot produce differences that grow in this way.
Frequently asked questions
What is the correct answer to this question?
(a_n=5n^2+2)
Why is this the correct answer?
The terms do not have a constant first difference: the differences are 15, 25, and 35. However, these differences increase by 10, suggesting a quadratic rule. The proposed expression \(5n^2+2\) can be checked directly by substituting the small positive indices. Testing the first few positions is an efficient way to verify a general term when answer choices are provided.
For \(n=1\), \(5(1)^2+2=7\); for \(n=2\), \(5(2)^2+2=22\); for \(n=3\), it gives 47; and for \(n=4\), it gives 82. Thus it reproduces every displayed term, so option A is correct. The linear choices cannot produce differences that grow in this way.
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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