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Class 9MathematicsSequences and Progressionsnth termExpertLevel 56
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If \(a_n=3\cdot2^{n-1}\), what will be \(a_7\)?

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Answer and explanation

Correct answer: 192

Substitute \(n=7\) in \(a_n=3\cdot2^{n-1}\): \(a_7=3\cdot2^{7-1}=3\cdot2^6=3\cdot64=192\). Therefore, 192 is the correct option. The value 96 results from incorrectly using the exponent 5 instead of 6. Exam tip: simplify the exponent \(n-1\) before evaluating the power.

Related tags

Sequences And ProgressionsNth TermGeometric SequenceExponentsClass 9 Mathematics

Frequently asked questions

What is the correct answer to this question?

192

Why is this the correct answer?

Substitute \(n=7\) in \(a_n=3\cdot2^{n-1}\): \(a_7=3\cdot2^{7-1}=3\cdot2^6=3\cdot64=192\). Therefore, 192 is the correct option. The value 96 results from incorrectly using the exponent 5 instead of 6. Exam tip: simplify the exponent \(n-1\) before evaluating the power.

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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  1. 1In the sequence \((1,4,9,16,\ldots)\), what is the difference between the 15th term and the 14th term?
  2. 2What is the 25th term of the sequence \((-5,-1,3,7,\ldots)\)?
  3. 3If aₙ = n³ − n, what will be the value of a₇ − a₅?
  4. 4What will be the 12th term in the sequence (3, 5, 9, 15, 23, ...)?
  5. 5If a_n = n(n + 2), what will be the value of a_11 − a_8?
  6. 6If a_n = n^2 + 5n - 2, which term is equal to 148?
  7. 7The sequence (3, 8, 15, 24, …) has general term a_n = n² + 2n. Which term is 168?
  8. 8If a_n = n³ + n², what will be the value of a_6 − a_4?
  9. 9If a_n = 4n² − 1, which term is 575?
  10. 10If a_n = n(n + 3), which term is 130?
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