If aₙ = n²+n+3, what is the value of a₁₀−a₉?
Answer and explanation
Correct answer: 20
The governing concept is substituting term numbers into an explicit sequence rule and then subtracting. For n=10, a₁₀=10²+10+3=100+10+3=113. For n=9, a₉=9²+9+3=81+9+3=93. Therefore a₁₀−a₉=113−93=20, so option C is correct. The result can also be checked directly by simplifying: (10²+10+3)−(9²+9+3)=100+10−81−9=20, because the constant terms cancel. The values 18, 19, and 21 arise from arithmetic or substitution mistakes, such as using an incorrect square or omitting one of the linear terms. Calculating both terms carefully avoids those errors.
Frequently asked questions
What is the correct answer to this question?
20
Why is this the correct answer?
The governing concept is substituting term numbers into an explicit sequence rule and then subtracting. For n=10, a₁₀=10²+10+3=100+10+3=113. For n=9, a₉=9²+9+3=81+9+3=93. Therefore a₁₀−a₉=113−93=20, so option C is correct. The result can also be checked directly by simplifying: (10²+10+3)−(9²+9+3)=100+10−81−9=20, because the constant terms cancel. The values 18, 19, and 21 arise from arithmetic or substitution mistakes, such as using an incorrect square or omitting one of the linear terms. Calculating both terms carefully avoids those errors.
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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