Question

Write the first four terms of the sequence defined by each of the following recursive formulas.

Answer 1

Answer:

First sequence: 3, 0, -3, -6

Second sequence: 2, 2.5, 3, 3.5

Step-by-step explanation:

$\left\{\begin{array}{ccc}a_1=3\\a_n=a_{n-1}-3\end{array}\right\\\\\text{Put n = 2, n = 3 and n = 4 to the formula of}\ a_n:\\\\a_1=3\\a_2=a_{2-1}-3=a_1-3\to a_2=3-3=0\\a_3=a_2-1\to a_3=0-3=-3\\a_4=a_3-3\to a_4=-3-3=-6$

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$\left\{\begin{array}{ccc}a_1=2\\a_n=a_{n-1}+0.5\end{array}\right\\\\a_1=2\\a_2=a_{2-1}+0.5=a_1+0.5\to a_2=2+0.5=2.5\\a_3=a_2+0.5\to a_3=2.5+0.5=3\\a_4=a_3+0.5\to a_4=3+0.5=3.5$

Answer 2

Answer:

First equation : 3, 0, -3, -6

Second equation : 2, 2.5, 3, 3.5

Step-by-step explanation:

What the first equation is basically saying is subtract 3 each time.

What the second equation is basically saying is add 0.5 each time.

Then we just add/subtract to find the first four terms.