To find the fifteenth term of the arithmetic sequence, we need to determine the first term ($a$) and the common difference ($d$).

Step 1: General formula for an arithmetic sequence

The $n$-th term of an arithmetic sequence is given by: $a_n = a + (n-1)d$ Where:

• $a$ is the first term,
• $d$ is the common difference,
• $n$ is the term number.

Step 2: Write equations for the given terms

We know:

• The seventh term ($a_7$) is 39: a + 6d = 39 \tag{1}
• The twenty-seventh term ($a_{27}$) is 139: a + 26d = 139 \tag{2}

Step 3: Solve for $a$ and $d$

Subtract equation (1) from equation (2) to eliminate $a$: $(a + 26d) - (a + 6d) = 139 - 39$ $20d = 100$ $d = 5$

Substitute $d = 5$ into equation (1) to solve for $a$: $a + 6(5) = 39$ $a + 30 = 39$ $a = 9$

Step 4: Find the fifteenth term

The fifteenth term ($a_{15}$) is: $a_{15} = a + 14d$ Substitute $a = 9$ and $d = 5$: $a_{15} = 9 + 14(5)$ $a_{15} = 9 + 70 = 79$

Final Answer:

The fifteenth term of the sequence is: $\boxed{79}$

Would you like a detailed explanation of the steps or additional examples?

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Related Questions:

1. What is the sum of the first 15 terms of this arithmetic sequence?
2. What is the 50th term of this sequence?
3. How can we verify if a given number is part of this sequence?
4. How do arithmetic sequences relate to linear functions?
5. Can you derive the formula for the $n$-th term of an arithmetic sequence?

Tip:

When solving arithmetic sequence problems, always write out the general term formula clearly before substituting values—it avoids mistakes.