Calculate: \( a_5 = 3 \times 25 - 10 + 1 = 75 - 10 + 1 = 66 \).
["# How to Calculate ( a_5 = 3 \ imes 25 - 10 + 1 = 66 ): A Simple Step-by-Step Guide", "Calculating expressions step by step is a fundamental math skill that helps in understanding algebra, solving equations, and building confidence in mathematical reasoning. In this article, we will break down the calculation of ( a_5 = 3 \ imes 25 - 10 + 1 ) to show exactly how to reach the correct result: 66. This clear, itemized approach not only solves the expression but also teaches a useful method for similar arithmetic problems.", "## Step 1: Understand the Expression", "The expression given is:\n[\na_5 = 3 \ imes 25 - 10 + 1\n]", "This is an arithmetic expression involving multiplication, subtraction, and addition—common operations in algebra and basic math. The variable ( a_5 ) represents the result of the entire expression when evaluated.", "## Step 2: Perform Multiplication First", "In mathematical order, multiplication is performed before subtraction and addition. According to the order of operations (PEMDAS/BODMAS), we calculate:\n[\n3 \ imes 25\n]\nCalculating this:\n[\n3 \ imes 25 = 75\n]", "Now update the expression:\n[\na_5 = 75 - 10 + 1\n]", "## Step 3: Apply Subtraction from Left to Right", "Next, subtract 10 from 75:\n[\n75 - 10 = 65\n]", "The expression now becomes:\n[\na_5 = 65 + 1\n]", "## Step 4: Finish with Addition", "Finally, add 1:\n[\n65 + 1 = 66\n]", "## Final Result", "Thus,\n[\na_5 = 66\n]", "## Why This Step-by-Step Method Matters", "Breaking down expressions into individual operations helps prevent errors and strengthens foundational math skills. Whether in homework, standardized tests, or real-world applications, understanding each step makes solving complex problems easier. Mastering this process allows students and learners to apply similar logic to algebraic expressions and equations.", "## Summary", "- Multiply first: ( 3 \ imes 25 = 75 )\n- Subtract: ( 75 - 10 = 65 )\n- Add: ( 65 + 1 = 66 )\n- Final result: ( a_5 = 66 )", "By following each operation clearly, you ensure accuracy and clarity in calculations.", "---", "Key takeaway:\nAlways follow the correct order of operations—eliminate parentheses first, then exponents, multiply/divide from left to right, and add/subtract from left to right. With practice, calculating expressions like ( 3 \ imes 25 - 10 + 1 ) becomes intuitive."]
