If a_n = 2^n + 3n, what will be the first four terms?
Answer and explanation
Correct answer: (5, 10, 17, 28)
The governing concept is evaluating an explicit formula at successive positive integer indices. Compute each term carefully, remembering that 2^n is an exponential part and 3n is a separate linear part. For n = 1, a_1 = 2^1 + 3(1) = 2 + 3 = 5. For n = 2, a_2 = 2^2 + 3(2) = 4 + 6 = 10. For n = 3, a_3 = 8 + 9 = 17. For n = 4, a_4 = 16 + 12 = 28. Hence the first four terms are (5, 10, 17, 28), so option A is correct. Option B effectively undercounts the linear contribution, while C and D introduce incorrect additions at later indices. The exponent applies only to 2, not to the entire expression.
Frequently asked questions
What is the correct answer to this question?
(5, 10, 17, 28)
Why is this the correct answer?
The governing concept is evaluating an explicit formula at successive positive integer indices. Compute each term carefully, remembering that 2^n is an exponential part and 3n is a separate linear part. For n = 1, a_1 = 2^1 + 3(1) = 2 + 3 = 5. For n = 2, a_2 = 2^2 + 3(2) = 4 + 6 = 10. For n = 3, a_3 = 8 + 9 = 17. For n = 4, a_4 = 16 + 12 = 28. Hence the first four terms are (5, 10, 17, 28), so option A is correct. Option B effectively undercounts the linear contribution, while C and D introduce incorrect additions at later indices. The exponent applies only to 2, not to the entire expression.
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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