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.
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