Solve the following
Question:

Let < an > be a sequence defined by

a1 = 3

and, an = 3an − 1 + 2, for all n > 1

Find the first four terms of the sequence.

Solution:

Given:

a1 = 3

And, an = 3an − 1 + 2 for all n > 1

$a_{2}=3 a_{2-1}+2=3 a_{1}+2=11$

$a_{3}=3 a_{3-1}+2=3 a_{2}+2=35$

$a_{4}=3 a_{4-1}+2=3 a_{3}+2=107$

Thus, the first four terms of the sequence are $3,11,35,107$.

 

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