To find the first three terms of the arithmetic sequence given by the recursive formula, we need to start with the first term and then apply the recurrence relation to calculate the subsequent terms.
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The first term \( a_1 \) is given as: \[ a_1 = -5 \]
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The recursive formula states that: \[ a_n = a_{n-1} + 4 \] This means each term is obtained by adding 4 to the previous term.
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Now, let's calculate the second term \( a_2 \): \[ a_2 = a_1 + 4 = -5 + 4 = -1 \]
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Next, we will calculate the third term \( a_3 \): \[ a_3 = a_2 + 4 = -1 + 4 = 3 \]
So, the first three terms of the sequence are:
- \( a_1 = -5 \)
- \( a_2 = -1 \)
- \( a_3 = 3 \)
Thus, the first three terms of the sequence are \( -5, -1, 3 \).
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