Write the next three terms of the arithmetic sequence. First term: $108$108​  Common difference:  $23$23​The next three terms are  , , and .

Break Down the Problem

1. Identify the first term of the arithmetic sequence.
2. Use the common difference to find the next three terms.

Relevant Concepts

The $n$-th term of an arithmetic sequence can be calculated using the formula: $a_n = a_1 + (n - 1) \cdot d$ where:

• $a_n$ is the $n$-th term,
• $a_1$ is the first term,
• $d$ is the common difference.

Analysis and Detail

1. First term $a_1 = 108$.
2. Common difference $d = 23$.

Now, we can find the next three terms:

• Second Term ($a_2$): $a_2 = a_1 + d = 108 + 23 = 131$
• Third Term ($a_3$): $a_3 = a_1 + 2d = 108 + 2 \cdot 23 = 108 + 46 = 154$
• Fourth Term ($a_4$): $a_4 = a_1 + 3d = 108 + 3 \cdot 23 = 108 + 69 = 177$

Verify and Summarize

The calculated terms are $131$, $154$, and $177$. We verified the calculations by applying the common difference after the first term.

Final Answer

The next three terms of the arithmetic sequence are $131$, $154$, and $177$.