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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.
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Solution
Given:
a1 = 3
And, an = 3an − 1 + 2 for all n > 1
\[a_2 = 3 a_{2 - 1} + 2 = 3 a_1 + 2 = 11\]
\[ a_3 = 3 a_{3 - 1} + 2 = 3 a_2 + 2 = 35\]
\[ a_4 = 3 a_{4 - 1} + 2 = 3 a_3 + 2 = 107\]
\[\text { Thus, the first four terms of the sequence are } 3, 11, 35, 107 .\]
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