Questions: Write the first six terms of the arithmetic sequence with the first term, a₁=4, and common difference, d=-8. The first six terms are a₁= a₂= a₃= a₄= a₅= and a₆= .

Write the first six terms of the arithmetic sequence with the first term, a₁=4, and common difference, d=-8.

The first six terms are a₁= a₂= a₃= a₄= a₅= and a₆= .

Transcript text: Write the first six terms of the arithmetic sequence with the first term, $a_{1}=4$, and common difference, $d=-8$. The first six terms are $a_{1}=$ $\square$ $a_{2}=\square$ $\square$ $a_{3}=$ $\square$ $a_{4}=$ $\square$ $a_{5}=$ $\square$ and $\mathrm{a}_{6}=$ $\square$.

Solution

Solution Steps

To find the first six terms of an arithmetic sequence, we start with the first term $ a_1 = 4 $ and use the common difference $ d = -8 $. Each subsequent term is found by adding the common difference to the previous term. Therefore, the $ n $-th term can be calculated using the formula $ a_n = a_1 + (n-1) \times d $.

Step 1: Identify the First Term and Common Difference

The first term of the arithmetic sequence is given as $ a_1 = 4 $ and the common difference is $ d = -8 $.

Step 2: Calculate the Subsequent Terms

To find each term in the sequence, use the formula for the $ n $-th term of an arithmetic sequence: \[ a_n = a_1 + (n-1) \times d \] Calculate each of the first six terms: