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Class 9MathematicsSequences and ProgressionsExplicit or general ruleEasyLevel 51
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If (a_n=2^{n+1}), what is the value of (a_3)?

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Answer and explanation

Correct answer: \(16\)

Given \(a_n=2^{n+1}\), substitute \(n=3\): \(a_3=2^{3+1}=2^4=16\). Hence, \(16\) is correct. \(8\) would result from using \(2^3\) and incorrectly ignoring the \(+1\) in the exponent. Exam tip: substitute the term number into the entire exponent before simplifying.

Related tags

SequencesProgressionsExplicit RuleGeneral TermExponentsClass 9

Frequently asked questions

What is the correct answer to this question?

\(16\)

Why is this the correct answer?

Given \(a_n=2^{n+1}\), substitute \(n=3\): \(a_3=2^{3+1}=2^4=16\). Hence, \(16\) is correct. \(8\) would result from using \(2^3\) and incorrectly ignoring the \(+1\) in the exponent. Exam tip: substitute the term number into the entire exponent before simplifying.

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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  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?
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  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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