Let's solve the equation for \( a_5 \) step by step.

The given equation is:
\[ a_5 = 5(5)2 - 1 \]

First, calculate the expression inside the parentheses:
\[ a_5 = 5 \times 5 \times 2 - 1 \]

Now, perform the multiplication:
\[ a_5 = 5 \times 10 - 1 \]

Next, subtract 1 from the product:
\[ a_5 = 50 - 1 \]

So, the final value is:
\[ a_5 = 49 \]

Would you like further details or have any questions?

Here are some related questions for further exploration:

1. What if the equation were \( a_5 = 5(5)^2 - 1 \)? How would that change the result?
2. How does the formula \( a_n = n(n)2 - 1 \) generalize for different values of \( n \)?
3. What if the subtraction was replaced by addition, as in \( a_5 = 5(5)2 + 1 \)?
4. Can you find the next term, \( a_6 \), using the same pattern?
5. How would the problem change if \( a_5 \) included a different multiplier, like \( a_5 = 5(5)3 - 1 \)?
6. What if the expression involved division, such as \( a_5 = 5(5/2) - 1 \)?
7. How would changing the order of operations, like using \( 5 \times (5 \times 2 - 1) \), affect the outcome?
8. Can this type of formula be used to model any real-world phenomena?

**Tip:** When working with similar equations, always check if the pattern changes or remains consistent, especially if variables or constants are adjusted.

Learn how to solve the arithmetic expression 5(5)2 - 1 with a detailed step-by-step solution. This problem covers basic arithmetic operations and order of operations. Suitable for students in Grades 5-6.

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