Question

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

Answer 1

`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

Answer 2

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