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Find the first five terms of the sequence given by a 1 = 2, a n = 3 a n -1 - 1.

2 Answers

5 votes

Answer:


a_(1)\\\\ = 2


a_(2\\)\\\\ = 5


a_(3\\)\\\\ = 14


a_(4\\)\\\\ = 41


a_(5\\)\\\\ = 122

Explanation:

If I've properly understood:


a_(1)\\\\ = 2


a_(n) = 3 a_(n-1)\\ - 1

so, the first 5 terms are:


a_(1)\\\\ = 2


a_(2\\)\\\\ = 3. 2 - 1 = 5


a_(3\\)\\\\ = 3. 5 - 1 = 14


a_(4\\)\\\\ = 3. 14 - 1 = 41


a_(5\\)\\\\ = 3. 41 - 1 = 122

User Hjaved
by
8.6k points
0 votes

Answer:

2, 5, 14, 41, 122

Explanation:

Using the recursive rule with a₁ = 2

a₂ = 3a₁ - 1 = 3(2) - 1 = 6 - 1 = 5

a₃ = 3a₂ - 1 = 3(5) - 1 = 15 - 1 = 14

a₄ = 3a₃ - 1 = 3(14) - 1 = 42 - 1 = 41

a₅ = 3a₄ - 1 = 3(41) - 1 = 123 - 1 = 122

The first 5 terms are 2, 5, 14, 41, 122

User Logan Murphy
by
7.5k points

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