To find the first five terms of the sequence defined by the formula \( a_n = -8n^2 - 3n + 2 \), we can substitute the values of \( n \) from 1 to 5 into the formula.
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For \( n = 1 \): \[ a_1 = -8(1^2) - 3(1) + 2 = -8(1) - 3 + 2 = -8 - 3 + 2 = -9 \]
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For \( n = 2 \): \[ a_2 = -8(2^2) - 3(2) + 2 = -8(4) - 3(2) + 2 = -32 - 6 + 2 = -36 \]
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For \( n = 3 \): \[ a_3 = -8(3^2) - 3(3) + 2 = -8(9) - 3(3) + 2 = -72 - 9 + 2 = -79 \]
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For \( n = 4 \): \[ a_4 = -8(4^2) - 3(4) + 2 = -8(16) - 3(4) + 2 = -128 - 12 + 2 = -138 \]
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For \( n = 5 \): \[ a_5 = -8(5^2) - 3(5) + 2 = -8(25) - 3(5) + 2 = -200 - 15 + 2 = -213 \]
Now we can summarize the first five terms of the sequence:
- \( a_1 = -9 \)
- \( a_2 = -36 \)
- \( a_3 = -79 \)
- \( a_4 = -138 \)
- \( a_5 = -213 \)
Thus, the first five terms of the sequence are: \[ -9, -36, -79, -138, -213 \]
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