If a_n = n^3 + n^2, what is a_5 : a_3?
Answer and explanation
Correct answer: 25 : 6
The governing concept is evaluation of an explicit sequence rule followed by simplification of a ratio. Substitute n = 5: a_5 = 5^3 + 5^2 = 125 + 25 = 150. Substitute n = 3: a_3 = 3^3 + 3^2 = 27 + 9 = 36. Therefore a_5 : a_3 = 150 : 36. Dividing both terms by their greatest common divisor, 6, gives 25 : 6. Hence option B is correct. Option A is the unsimplified ratio, option C reverses the order, and option D incorrectly compares only powers.
Frequently asked questions
What is the correct answer to this question?
25 : 6
Why is this the correct answer?
The governing concept is evaluation of an explicit sequence rule followed by simplification of a ratio. Substitute n = 5: a_5 = 5^3 + 5^2 = 125 + 25 = 150. Substitute n = 3: a_3 = 3^3 + 3^2 = 27 + 9 = 36. Therefore a_5 : a_3 = 150 : 36. Dividing both terms by their greatest common divisor, 6, gives 25 : 6. Hence option B is correct. Option A is the unsimplified ratio, option C reverses the order, and option D incorrectly compares only powers.
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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