Question:** A sequence starts with 2, and each subsequent term is the previous term multiplied by 3. What is the 5th term?

["Understanding Geometric Sequences: The 5th Term in a Sequence Starting with 2 and Tripled Each Time", "Have you ever wondered what happens when a number follows a consistent pattern—specifically, when each term is tripled to get the next? This classic example introduces the concept of a geometric sequence, a fundamental idea in mathematics with applications in finance, science, and computer algorithms.", "### What is a Geometric Sequence?", "A geometric sequence is a series of numbers where each term after the first is found by multiplying the previous term by a constant called the common ratio. In this case, the sequence starts at 2, and since each term is multiplied by 3, the common ratio is 3.", "---", "### The Basic Formula", "To find the nth term of a geometric sequence, you use the formula:", "[\na_n = a_1 \ imes r^{n-1}\n]", "Where:\n- (a_n) = the nth term\n- (a_1) = the first term\n- (r) = the common ratio\n- (n) = the term number", "---", "### Applying the Formula to Find the 5th Term", "Given:\n- (a_1 = 2)\n- (r = 3)\n- We want the 5th term → (n = 5)", "Plug values into the formula:", "[\na_5 = 2 \ imes 3^{5-1} = 2 \ imes 3^4\n]", "Calculate (3^4):", "[\n3^4 = 81\n]", "Now multiply:", "[\na_5 = 2 \ imes 81 = 162\n]", "---", "### Summary", "- The sequence begins: 2, 6, 18, 54, 162\n- The 5th term is 162", "Understanding geometric sequences helps in modeling exponential growth, like population increases, compound interest, and iterative processes in programming.", "---", "Key Takeaways:\n- A geometric sequence multiplies each term by a fixed ratio.\n- The nth term is found using (a_n = a_1 \ imes r^{n-1}).\n- For this sequence, the 5th term is 162.", "---", "Want to test your skills? Try finding the 6th and 7th terms using the same method!"]