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 nn-th term rule is given as 3n3^n, let’s calculate step by step:

  1. The nn-th term is expressed as 3n3^n.

  2. For the 5th term (n=5n = 5): 35=3×3×3×3×33^5 = 3 \times 3 \times 3 \times 3 \times 3

  3. Simplifying: 35=2433^5 = 243

Final Answer:

The 5th term of the sequence is 243.


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Related Questions:

  1. What would the 6th term of this sequence be?
  2. How can you identify if a number is a power of 3?
  3. What is the general formula for a geometric sequence?
  4. How do you determine the ratio in a geometric sequence?
  5. What are the first 7 terms of this sequence?

Tip:

For powers of a base (like 3n3^n), 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