If a_n = 4n^2 + 3n + 2, what is a_4 − a_1?
Answer and explanation
Correct answer: 69
The governing concept is evaluating an explicit formula at two indices and then subtracting in the stated order. First, a_4 = 4(4^2) + 3(4) + 2 = 4(16) + 12 + 2 = 78. Next, a_1 = 4(1^2) + 3(1) + 2 = 4 + 3 + 2 = 9. Therefore a_4 − a_1 = 78 − 9 = 69, so option B is correct. Option A can result from an arithmetic error in the quadratic term, while C and D arise from incorrect substitution or subtraction. Computing both sequence values separately helps preserve the required order.
Frequently asked questions
What is the correct answer to this question?
69
Why is this the correct answer?
The governing concept is evaluating an explicit formula at two indices and then subtracting in the stated order. First, a_4 = 4(4^2) + 3(4) + 2 = 4(16) + 12 + 2 = 78. Next, a_1 = 4(1^2) + 3(1) + 2 = 4 + 3 + 2 = 9. Therefore a_4 − a_1 = 78 − 9 = 69, so option B is correct. Option A can result from an arithmetic error in the quadratic term, while C and D arise from incorrect substitution or subtraction. Computing both sequence values separately helps preserve the required order.
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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