The 5th term is \(2 \times 3^4 = 2 \times 81 = 162\).

["Understanding the 5th Term in the Geometric Sequence: (2 \ imes 3^4 = 162)", "When exploring geometric sequences, one common calculation involves finding specific terms using the formula for each position. One notable instance is determining the 5th term of a sequence defined by (2 \ imes 3^n). Let’s break down how this term equals 162, why this formula works, and its educational value.", "### What Is the 5th Term in Geometric Sequences?", "In a geometric sequence, each term is derived by multiplying the previous term by a constant ratio. If a sequence begins with (a_1 = 2) and a common ratio (r = 3), the (n)-th term follows the formula:", "[\na_n = a_1 \ imes r^{n-1}\n]", "For the 5th term ((n = 5)):", "[\na_5 = 2 \ imes 3^{5 - 1} = 2 \ imes 3^4\n]", "### Calculating (3^4) and Finding the Term", "We compute (3^4):", "[\n3^4 = 3 \ imes 3 \ imes 3 \ imes 3 = 81\n]", "Now, plug in the value:", "[\na_5 = 2 \ imes 81 = 162\n]", "Thus, the 5th term of the sequence is 162.", "### Why This Calculation Matters in Education and Beyond", "Understanding formulas like (2 \ imes 3^n) helps learners grasp exponential growth — a concept key in mathematics, science, finance, and technology. For instance:", "- Exponential Growth: From a starting value tripling each period, see how quickly values escalate.\n- Financial Modeling: Used in calculating compound interest or investment growth.\n- Science: Describing population growth, decay rates, or scientific measurements.", "### Summary", "- The 5th term of the sequence starting at 2 with a ratio of 3 is (2 \ imes 3^4 = 162).\n- The formula combines the first term with powers of the common ratio.\n- Recognizing these patterns supports deeper math literacy and practical problem-solving.", "If you’re learning algebra or exploring sequences, mastering such term calculations is fundamental. Remember: elimination and simplification under exponent rules unlock efficient and accurate results!", "[\n\boxed{2 \ imes 3^4 = 162}\n]"]