A sequence starts with 5 and each subsequent term is obtained by multiplying the previous term by 3. Find the 6th term in the sequence.
["Title: The Simple Geometric Sequence: Finding the 6th Term When Starting with 5 and Multiplying by 3 Each Time", "Meta Description: Explore a structured arithmetic pattern where each term is three times the previous. Learn how to calculate and find the 6th term in this easy geometric sequence.", "---", "### Introduction to Geometric Sequences", "A geometric sequence is a list of numbers where each term after the first is found by multiplying the previous term by a constant ratio. This type of sequence is widely used in mathematics, science, finance, and computer science because of its predictable pattern and rapid growth.", "In this article, we focus on a straightforward geometric sequence that starts with 5 and each subsequent term is obtained by multiplying by 3. This means the sequence grows quickly—doubling every step, but multiplied by 3 each time.", "---", "### Understanding the Pattern", "Let’s break down the sequence step by step:", "- 1st term = 5\n- 2nd term = 5 × 3 = 15\n- 3rd term = 15 × 3 = 45\n- 4th term = 45 × 3 = 135\n- 5th term = 135 × 3 = 405\n- 6th term = 405 × 3 = 1215", "Each term is generated by multiplying the previous number by 3. This fixed multiplication factor defines a geometric progression with the common ratio ( r = 3 ).", "---", "### Formula for the nth Term", "For any geometric sequence, the ( n )-th term can be calculated using the formula:", "[\na_n = a_1 \ imes r^{(n-1)}\n]", "Where:\n- ( a_n ) = nth term\n- ( a_1 ) = first term = 5\n- ( r ) = common ratio = 3\n- ( n ) = position of the term", "To find the 6th term:", "[\na_6 = 5 \ imes 3^{(6-1)} = 5 \ imes 3^5\n]", "Calculate ( 3^5 ):\n[\n3^5 = 3 \ imes 3 \ imes 3 \ imes 3 \ imes 3 = 243\n]", "Now multiply:\n[\na_6 = 5 \ imes 243 = 1215\n]", "---", "### Conclusion", "The 6th term in the sequence beginning with 5 and multiplying by 3 at each step is 1215. This example demonstrates how simple geometric progressions produce rapidly increasing values and how powerful exponential growth begins with a fixed multiplicative rule.", "Whether you're solving math problems, analyzing patterns, or modeling real-world scenarios, understanding such sequences lays a strong foundation in mathematics and beyond.", "Keywords: geometric sequence, 5, multiply by 3, 6th term, exponential growth, mathematical pattern, sequence formula, 3^5, math tutorial"]
