Question

What is the term rule for 3, 8, 23, 68

Answer 1

Step-by-step explanation:

Hint. You may observe that

an−

1

2

=3(an−1−

1

2

),a0=3,

then you may easily obtain an explicit formula for an−

1

2

thus an explicit formula for an.

Addendum. From an=3an−1−1, we are looking for a real number α such that

an+α=3(an−1+α)

then replacing an with 3an−1−1 and expanding (1) gives

3an−1−1+α=3an−1+3α

and (2) rewrites −1+α=3α from which you deduce α=−

1

2

. The first term of the auxiliary sequence is a0−

1

2

=3−

1

2

=

5

2

. Thus from (1) you get an−

1

2

=

5

2

×3n.