What is the answer to 3 9 27 81 243

General
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what is the answer to 3 9 27 81 243

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What is the answer to 3 9 27 81 243?

Answer:

To understand the sequence of numbers presented—3, 9, 27, 81, 243—it’s important to recognize the pattern they follow. This sequence is an example of a geometric progression, where each term after the first is found by multiplying the previous term by a constant factor.

Step 1: Identify the Pattern

  1. Sequence: 3, 9, 27, 81, 243
  2. Constant Ratio: To find the ratio, divide any term by the previous term. For example:
    • 9 \div 3 = 3
    • 27 \div 9 = 3
    • 81 \div 27 = 3
    • 243 \div 81 = 3

The constant ratio between successive terms is 3.

Step 2: Understand the Geometric Progression

A geometric sequence or progression is one where each term is the product of the previous term and a fixed non-zero number called the common ratio. Here, the common ratio is 3.

  • First Term (a): The first term of the sequence is 3.
  • Common Ratio (r): The common ratio is also 3.

The general formula for the n^{th} term (T_n) of a geometric sequence is:

T_n = a \cdot r^{(n-1)}

Where:

  • a is the first term
  • r is the common ratio
  • n is the term number

Step 3: Calculation

To find the n^{th} term for any specified term, you can apply the formula.

For the next term in the sequence (after 243), it would be:

  • Current term (5th term): 243

  • Next term (T_6):

    T_6 = 243 \cdot 3 = 729

Final Answer:

The sequence 3, 9, 27, 81, 243 is a geometric progression with a common ratio of 3. The next term in the sequence is 729.