Questions: For the sequence (an=6-5 cdot(n-1)), its first term is (square) its second term is (square) its third term is (square) its fourth term is (square) ; its fifth term is (square) ; its common difference (d=) (square)

Solution Steps

To solve for the terms of the sequence and the common difference, we will:

1. Substitute $n = 1, 2, 3, 4, 5$ into the given formula $a_n = 6 - 5 \cdot (n-1)$ to find the first five terms.
2. Identify the common difference $d$ by subtracting the first term from the second term.

Using the formula for the sequence $a_n = 6 - 5 \cdot (n-1)$, we calculate the first five terms:

• For $n = 1$: $$a_1 = 6 - 5 \cdot (1-1) = 6 - 0 = 6$$

• For $n = 2$: $$a_2 = 6 - 5 \cdot (2-1) = 6 - 5 = 1$$

• For $n = 3$: $$a_3 = 6 - 5 \cdot (3-1) = 6 - 10 = -4$$

• For $n = 4$: $$a_4 = 6 - 5 \cdot (4-1) = 6 - 15 = -9$$

• For $n = 5$: $$a_5 = 6 - 5 \cdot (5-1) = 6 - 20 = -14$$

Thus, the first five terms are $6, 1, -4, -9, -14$.

The common difference $d$ is calculated as follows: $$d = a_2 - a_1 = 1 - 6 = -5$$

Final Answer