If aₙ = 3n² − 2n + 1, what is the value of a₈ − a₅?
Answer and explanation
Correct answer: 111
The governing concept is evaluating an explicit sequence formula at two indices and subtracting the results. First calculate a₈: 3(8²) − 2(8) + 1 = 3 × 64 − 16 + 1 = 192 − 16 + 1 = 177. Next calculate a₅: 3(5²) − 2(5) + 1 = 3 × 25 − 10 + 1 = 75 − 10 + 1 = 66. Hence a₈ − a₅ = 177 − 66 = 111. Therefore option D is correct. Computing both terms separately avoids confusing the index with the value. The other choices do not result from the correct substitution and subtraction.
Frequently asked questions
What is the correct answer to this question?
111
Why is this the correct answer?
The governing concept is evaluating an explicit sequence formula at two indices and subtracting the results. First calculate a₈: 3(8²) − 2(8) + 1 = 3 × 64 − 16 + 1 = 192 − 16 + 1 = 177. Next calculate a₅: 3(5²) − 2(5) + 1 = 3 × 25 − 10 + 1 = 75 − 10 + 1 = 66. Hence a₈ − a₅ = 177 − 66 = 111. Therefore option D is correct. Computing both terms separately avoids confusing the index with the value. The other choices do not result from the correct substitution and subtraction.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Sequences and Progressions. Topic: nth term.
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