A geometric sequence has a first term of 3 and a common ratio of 2. What is the 5th term?
["Understanding Geometric Sequences: Solving for the 5th Term with a First Term of 3 and a Common Ratio of 2", "A geometric sequence is a fascinating mathematical pattern where each term after the first is found by multiplying the previous term by a consistent value called the common ratio. Whether you're studying math, engineering, computer science, or finance, understanding geometric sequences is essential. In this article, we’ll explore a specific geometric sequence — one with a first term of 3 and a common ratio of 2 — and walk through how to find the 5th term.", "---", "### What Is a Geometric Sequence?", "A geometric sequence follows the general rule:", "$$\na_n = a_1 \ imes r^{(n-1)}\n$$", "Where:\n- $ a_n $ = the $ n $th term\n- $ a_1 $ = the first term\n- $ r $ = the common ratio\n- $ n $ = the term number", "---", "### Given Values", "For the sequence in focus:\n- $ a_1 = 3 $\n- $ r = 2 $\n- We want to find the 5th term, so $ n = 5 $", "---", "### Step-by-Step Calculation", "Plug the known values into the formula:", "$$\na_5 = 3 \ imes 2^{(5-1)} = 3 \ imes 2^4\n$$", "Calculate the exponent:", "$$\n2^4 = 16\n$$", "Now multiply:", "$$\na_5 = 3 \ imes 16 = 48\n$$", "---", "### ✅ Final Answer", "The 5th term of the geometric sequence with first term 3 and common ratio 2 is 48.", "---", "### Why This Sequence Matters", "Geometric sequences appear in everyday and professional contexts — from computing compound interest and population growth to designing algorithms and modeling physics. Knowing how to find specific terms, like the 5th term here, helps in solving real-world problems efficiently.", "---", "### Practice Tip", "To master geometric sequences:\n- Use the formula $ a_n = a_1 \ imes r^{(n-1)} $ repeatedly\n- Practice with different starting terms and ratios\n- Try deriving the nth term formula manually", "Understanding geometric sequences not only boosts math skills but also strengthens logical reasoning — a valuable asset in many technical fields.", "---", "Keywords: geometric sequence, nth term, common ratio, math tutorial, exponential growth, sequence calculation, algebra problem, exponential formula\nMeta Description: Learn to find the 5th term in a geometric sequence with a first term of 3 and a common ratio of 2 using the formula aₙ = a₁ × rⁿ⁻¹. Step-by-step solution included."]
