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Subjects
Class 9MathematicsSequences and ProgressionsExplicit or general ruleExpertLevel 49
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If (a_n=(n+1)^3-n), what is the value of (a_4)?

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Answer and explanation

Correct answer: 121

Given \(a_n=(n+1)^3-n\), substitute \(n=4\): \(a_4=(4+1)^3-4=5^3-4=125-4=121\). Therefore, 121 is the correct option. 123 would result from an incorrect subtraction. Exam tip: substitute the term number first, evaluate the exponent, and then subtract.

Related tags

SequencesProgressionsExplicit RuleSubstitutionAlgebraClass 9

Frequently asked questions

What is the correct answer to this question?

121

Why is this the correct answer?

Given \(a_n=(n+1)^3-n\), substitute \(n=4\): \(a_4=(4+1)^3-4=5^3-4=125-4=121\). Therefore, 121 is the correct option. 123 would result from an incorrect subtraction. Exam tip: substitute the term number first, evaluate the exponent, and then subtract.

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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10 more MCQs
  1. 1For the sequence 2, 5, 10, 17, 26, ..., the nth term is a_n = n² + 1. What is the value of a_12 − a_10?
  2. 2For the sequence 6, 14, 26, 42, ..., a_n = 2n² + 2n + 2. What is the value of a_15 - a_13?
  3. 3If a_n = (-1)^n(n + 1), what will be the value of a_7 + a_8?
  4. 4What will be the next term in the sequence (1, 2, 6, 24, 120, …)?
  5. 5If a_n = 5n + (−1)^n, what will be the value of a_10 − a_9?
  6. 6If a_n = 4n^2 + 2n - 3, what will be the value of a_11?
  7. 7If a_n = (-1)^(n+1)(2n+3), what will be the value of a_8 + a_9?
  8. 8If a_n = n^2 + 6n + 5, which term is 252?
  9. 9What is the general term of the sequence (3, 6, 9, 12, …)?
  10. 10Which explicit rule is correct for the sequence (5, 10, 15, 20, …)?
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