Math Problem Statement
Work out the 5th term of the sequence where the nth term rule is 3^n. The first few terms are 3, 9, 27...
Solution
To determine the 5th term of the sequence where the -th term rule is given as , let’s calculate step by step:
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The -th term is expressed as .
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For the 5th term ():
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Simplifying:
Final Answer:
The 5th term of the sequence is 243.
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Related Questions:
- What would the 6th term of this sequence be?
- How can you identify if a number is a power of 3?
- What is the general formula for a geometric sequence?
- How do you determine the ratio in a geometric sequence?
- What are the first 7 terms of this sequence?
Tip:
For powers of a base (like ), each term is obtained by multiplying the previous term by the base (here, 3).
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Math Problem Analysis
Mathematical Concepts
Exponents
Powers of a Number
Sequences
Formulas
nth term rule: 3^n
Theorems
Exponentiation rules
Suitable Grade Level
Grade 6-8