SOLUTION: the sequence is defined recursively. Write the first five terms. a1=2, a2=5; an=an-2

SOLUTION: the sequence is defined recursively. Write the first five terms. a1=2, a2=5; an=an-2 - 3an-1.

Question 614863: the sequence is defined recursively. Write the first five terms.
a1=2, a2=5; an=an-2 - 3an-1.
Answer by ashipm01(26) (Show Source): You can put this solution on YOUR website!
The first two terms, a[1] and a[2], are the base cases. The following terms of the sequence are defined in terms of previous terms of the sequence (recursive sequence).

So the first two terms are given in the problem statement:
a[1] = 2
a[2] = 5

The next term, a[3], is given by a[3-2] - 3 * a[3-1].
a[3] = a[3-2] - 3 * a[3-1]
= a[1] - 3 * a[2]
= 2 - (3*5)
= -13

Then a[4] is given in terms of a[4-2] and q[4-1]:
a[4] = a[4-2] - 3 * a[4-1]
= a[2] - 3 * a[3]
= 5 - (3 * -13)
= 44

Likewise, a[5] is given in terms of a[5-2] and a[5-1]:
a[5] = a[5-2] - 3 * a[5-1]
= a[3] - 3 * a[4]
= -13 - (3 * 44)
= -145

So the first five terms in the sequence are: {2, 5, -13, 44, -145}
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