Question

Determine is each statement is true or false. Select the true statements.
Responses
A The 15th term of the sequence An = 3n − 7 is 52.The 15th term of the sequence A n = 3n − 7 is 52.
B The 7th term of the sequence An = 4n + 3 is 31.The 7th term of the sequence A n = 4n + 3 is 31.
C The 9th term of the sequence 2, 6, 10, 14... is 32.The 9th term of the sequence 2, 6, 10, 14... is 32.
D The 10th term of the sequence −2, −5, −8, −11... is −29.The 10th term of the sequence −2, −5, −8, −11... is −29.
E The 8th term of the sequence An = −2n + 4 term 8 is −20.The 8th term of the sequence A n = −2n + 4 term 8 is −20.

Answer 1

To determine if each statement is true or false, we need to calculate the corresponding terms for each sequence.

**A**: The 15th term of the sequence \( A_n = 3n - 7 \).
\[
A_{15} = 3(15) - 7 = 45 - 7 = 38 \quad \text{(False)}
\]

**B**: The 7th term of the sequence \( A_n = 4n + 3 \).
\[
A_{7} = 4(7) + 3 = 28 + 3 = 31 \quad \text{(True)}
\]

**C**: The 9th term of the sequence \( 2, 6, 10, 14... \).
This is an arithmetic sequence where the first term is 2 and the common difference is 4. The nth term can be calculated as:
\[
A_n = 2 + (n-1) \cdot 4 = 2 + 4(n-1) = 4n - 2
\]
Calculating for n = 9:
\[
A_{9} = 4(9) - 2 = 36 - 2 = 34 \quad \text{(False)}
\]

**D**: The 10th term of the sequence \( -2, -5, -8, -11... \).
This is also an arithmetic sequence where the first term is -2 and the common difference is -3. Using the formula:
\[
A_n = -2 + (n-1)(-3) = -2 - 3(n-1)
\]
Calculating for n = 10:
\[
A_{10} = -2 - 3(9) = -2 - 27 = -29 \quad \text{(True)}
\]

**E**: The 8th term of the sequence \( A_n = -2n + 4 \).
\[
A_{8} = -2(8) + 4 = -16 + 4 = -12 \quad \text{(False)}
\]

To summarize, the true statements are:
- **B**: True
- **D**: True

Hence, the true statements are **B** and **D**.