If \(a_n=4\cdot3^{n-1}\), what is the fifth term?
Answer and explanation
Correct answer: 324
For the fifth term, substitute \(n=5\): \(a_5=4\cdot3^{5-1}=4\cdot3^4=4\cdot81=324\). Therefore, 324 is correct. The value 216 can result from incorrectly using \(3^3\) and miscounting the exponent \(n-1\). Exam tip: after substituting the term number, evaluate \(n-1\) before calculating the power.
Frequently asked questions
What is the correct answer to this question?
324
Why is this the correct answer?
For the fifth term, substitute \(n=5\): \(a_5=4\cdot3^{5-1}=4\cdot3^4=4\cdot81=324\). Therefore, 324 is correct. The value 216 can result from incorrectly using \(3^3\) and miscounting the exponent \(n-1\). Exam tip: after substituting the term number, evaluate \(n-1\) before calculating 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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