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