Question

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

Answer 1

Answer:

2, 5, 14, 41, 122

Step-by-step 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

Answer 2

Answer:

$a_{1}$ = 2

$a_{2\\}$ = 5

$a_{3\\}$ = 14

$a_{4\\}$ = 41

$a_{5\\}$ = 122

Step-by-step 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