Given the nth term formula, complete the first five terms of the sequence an = 5n2 -2n for n ≥ 1

To find the first five terms of the sequence given by the formula \(a_n = 5n^2 - 2n\) for \(n \geq 1\), we substitute \(n = 1, 2, 3, 4, \text{and} 5\) into the formula:

1. For \(n = 1\):
\[ a_1 = 5(1)^2 - 2(1) = 5 - 2 = 3 \]

2. For \(n = 2\):
\[ a_2 = 5(2)^2 - 2(2) = 5 \cdot 4 - 4 = 20 - 4 = 16 \]

3. For \(n = 3\):
\[ a_3 = 5(3)^2 - 2(3) = 5 \cdot 9 - 6 = 45 - 6 = 39 \]

4. For \(n = 4\):
\[ a_4 = 5(4)^2 - 2(4) = 5 \cdot 16 - 8 = 80 - 8 = 72 \]

5. For \(n = 5\):
\[ a_5 = 5(5)^2 - 2(5) = 5 \cdot 25 - 10 = 125 - 10 = 115 \]

Therefore, the first five terms of the sequence are \(3, 16, 39, 72, \text{and} 115\).

Would you like further details or have any questions?

Here are 5 numbered questions for you to ask:

1. How do you derive the nth term formula for an arithmetic sequence?
2. Can you explain how to find the derivative of a function?
3. How do you solve systems of linear equations using matrix methods?
4. What are the properties of logarithmic functions?
5. Can you show me how to integrate a given function?

Tip: When working with sequences, always verify your calculations by substituting values back into the formula to ensure accuracy.

Learn how to calculate the first five terms of the sequence 5n^2 - 2n with a detailed step-by-step solution. This problem involves using the nth term formula for sequences and covers key algebraic concepts. Suitable for students in Grades 7-9.

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