Question

write the first four terms of the sequence defined by each of the following recursive formulas.
$a_1 = 3$ and $a_n = a_{n-1} - 3$

$a_1 = 2$ and $a_n = a_{n-1} + 0.5$

Explanation:

Step1: Identify first term

$a_1 = 3$

Step2: Calculate second term

$a_2 = a_1 - 3 = 3 - 3 = 0$

Step3: Calculate third term

$a_3 = a_2 - 3 = 0 - 3 = -3$

Step4: Calculate fourth term

$a_4 = a_3 - 3 = -3 - 3 = -6$

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Step1: Identify first term

$a_1 = 2$

Step2: Calculate second term

$a_2 = a_1 + 0.5 = 2 + 0.5 = 2.5$

Step3: Calculate third term

$a_3 = a_2 + 0.5 = 2.5 + 0.5 = 3$

Step4: Calculate fourth term

$a_4 = a_3 + 0.5 = 3 + 0.5 = 3.5$

Answer:

First sequence: $3$, $0$, $-3$, $-6$
Second sequence: $2$, $2.5$, $3$, $3.5$