If a_n = n^2 + 6n + 5, what are the first four terms?
Answer and explanation
Correct answer: 12, 21, 32, 45
The governing concept is generating sequence terms from an explicit rule by using n = 1, 2, 3, and 4. For n = 1, a_1 = 1 + 6 + 5 = 12. For n = 2, a_2 = 4 + 12 + 5 = 21. For n = 3, a_3 = 9 + 18 + 5 = 32. For n = 4, a_4 = 16 + 24 + 5 = 45. Hence the first four terms are 12, 21, 32, 45, so A is correct. Starting with n = 0 would produce a different list, but sequence notation normally begins with n = 1 here; the other options reflect arithmetic or indexing errors.
Frequently asked questions
What is the correct answer to this question?
12, 21, 32, 45
Why is this the correct answer?
The governing concept is generating sequence terms from an explicit rule by using n = 1, 2, 3, and 4. For n = 1, a_1 = 1 + 6 + 5 = 12. For n = 2, a_2 = 4 + 12 + 5 = 21. For n = 3, a_3 = 9 + 18 + 5 = 32. For n = 4, a_4 = 16 + 24 + 5 = 45. Hence the first four terms are 12, 21, 32, 45, so A is correct. Starting with n = 0 would produce a different list, but sequence notation normally begins with n = 1 here; the other options reflect arithmetic or indexing errors.
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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