Math Problem Statement

Write the recursive formula for the sequence: 3, 6, 12, 24,...

Solution

The sequence provided is: 3,6,12,24,3, 6, 12, 24, \dots.

The numbers in this sequence are doubling each time:

  • 6=2×36 = 2 \times 3
  • 12=2×612 = 2 \times 6
  • 24=2×1224 = 2 \times 12

This indicates that the recursive formula involves multiplying the previous term by 2.

The recursive formula for this sequence is: a1=3;an=2an1 for n2.a_1 = 3; \quad a_n = 2a_{n-1} \text{ for } n \geq 2. This corresponds to the yellow box in the image.

Do you want further details or have any questions?

Here are 5 related questions:

  1. What is the next term in the sequence after 24?
  2. How would you describe the general formula for this sequence without recursion?
  3. Can you create a recursive formula for a sequence where the terms triple each time?
  4. What is the difference between recursive and explicit formulas?
  5. How would the sequence change if you multiplied by 3 instead of 2?

Tip: Recursive formulas express each term based on the previous one, making them powerful for sequences that follow a clear pattern.

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Math Problem Analysis

Mathematical Concepts

Sequences
Recursion
Geometric Progression

Formulas

Recursive formula: a_1 = 3; a_n = 2a_{n-1} for n ≥ 2

Theorems

Geometric sequence formula

Suitable Grade Level

Grades 8-10