Questions: Write the first six terms of the arithmetic sequence. a1 = 9/2, d = -1/2

Solution Steps

To find the first six terms of an arithmetic sequence, we use the formula for the nth term of an arithmetic sequence: \( a_n = a_1 + (n-1)d \). Here, \( a_1 \) is the first term and \( d \) is the common difference. We will calculate the first six terms using this formula.

Given: \[ a_1 = \frac{9}{2}, \quad d = -\frac{1}{2} \]

The formula for the \(n\)-th term of an arithmetic sequence is: \[ a_n = a_1 + (n-1)d \]

Using the formula, we calculate the first six terms: \[ \begin{align_} a_1 &= \frac{9}{2} = 4.5 \\ a_2 &= \frac{9}{2} + (2-1)\left(-\frac{1}{2}\right) = 4.5 - 0.5 = 4.0 \\ a_3 &= \frac{9}{2} + (3-1)\left(-\frac{1}{2}\right) = 4.5 - 1.0 = 3.5 \\ a_4 &= \frac{9}{2} + (4-1)\left(-\frac{1}{2}\right) = 4.5 - 1.5 = 3.0 \\ a_5 &= \frac{9}{2} + (5-1)\left(-\frac{1}{2}\right) = 4.5 - 2.0 = 2.5 \\ a_6 &= \frac{9}{2} + (6-1)\left(-\frac{1}{2}\right) = 4.5 - 2.5 = 2.0 \\ \end{align_} \]

Final Answer