If a_n = n(n + 2), what will be the value of a_11 − a_8?
Answer and explanation
Correct answer: 63
The governing concept is finding terms from an explicit nth-term formula. The expression must be evaluated separately at the two requested indices, while preserving the parentheses. For n = 11, a_11 = 11(11 + 2) = 11 × 13 = 143. For n = 8, a_8 = 8(8 + 2) = 8 × 10 = 80. Subtracting the actual term values gives a_11 − a_8 = 143 − 80 = 63. Therefore option A is correct. A frequent mistake is to subtract the indices, or to interpret n(n + 2) as n² + 2; neither follows the stated formula. Options B, C and D are therefore not supported by the required substitution and subtraction.
Frequently asked questions
What is the correct answer to this question?
63
Why is this the correct answer?
The governing concept is finding terms from an explicit nth-term formula. The expression must be evaluated separately at the two requested indices, while preserving the parentheses. For n = 11, a_11 = 11(11 + 2) = 11 × 13 = 143. For n = 8, a_8 = 8(8 + 2) = 8 × 10 = 80. Subtracting the actual term values gives a_11 − a_8 = 143 − 80 = 63. Therefore option A is correct. A frequent mistake is to subtract the indices, or to interpret n(n + 2) as n² + 2; neither follows the stated formula. Options B, C and D are therefore not supported by the required 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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