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Class 9MathematicsSequences and ProgressionsExplicit or general ruleExpertLevel 49
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If \(a_n=7\cdot2^{n-1}+4\), what is the value of \(a_5\)?

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Answer and explanation

Correct answer: 116

Substitute \(n=5\): \(a_5=7\cdot2^{5-1}+4=7\cdot2^4+4=7\cdot16+4=116\). Therefore, the correct answer is 116. The value 112 is only \(7\cdot16\); it misses the final \(+4\). Exam tip: evaluate \(n-1\) first, then calculate the power.

Related tags

SequencesProgressionsExplicit FormulaGeometric SequenceSubstitutionClass 9

Frequently asked questions

What is the correct answer to this question?

116

Why is this the correct answer?

Substitute \(n=5\): \(a_5=7\cdot2^{5-1}+4=7\cdot2^4+4=7\cdot16+4=116\). Therefore, the correct answer is 116. The value 112 is only \(7\cdot16\); it misses the final \(+4\). Exam tip: evaluate \(n-1\) first, then calculate the power.

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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