Let's solve the given equation step by step.

The equation is:
\[ a_4 = 4(4)2 - 1 \]

First, we calculate the expression inside the parentheses:
\[ a_4 = 4 \times 4 \times 2 - 1 \]

Now, let's perform the multiplication:
\[ a_4 = 4 \times 8 - 1 \]

Next, subtract 1 from the product:
\[ a_4 = 32 - 1 \]

So, the final value is:
\[ a_4 = 31 \]

Would you like further details or have any questions?

Here are some related questions for further exploration:

1. How would the equation change if the coefficient of the first term were different?
2. What if the parentheses included an additional term, like \(4(4+2)2 - 1\)?
3. Can you apply similar steps to solve \( a_n = 4n^2 - 1 \) for a general \( n \)?
4. What if the equation was \( a_4 = 4(4)(2) + 1 \) instead?
5. How does changing the operation from subtraction to addition affect the result?
6. What if the term inside the parentheses was squared, i.e., \( 4(4^2)2 - 1 \)?
7. How would the problem change if the expression was \( 4(4)2^2 - 1 \)?
8. Can you think of a real-life situation where this type of calculation might be useful?

**Tip:** Always pay attention to the order of operations in mathematical expressions (parentheses, exponents, multiplication/division, addition/subtraction) to ensure accurate results.

Learn how to solve the equation a4 = 4(4)2 - 1 with a detailed step-by-step solution. This problem covers arithmetic operations, including multiplication and subtraction. Suitable for students in Grades 5-6.

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