The sequence a1 = 6, an = 3an-1 can also be written as

The question as presented is incomplete, here is the complete question with the multiple choice:

The sequence a1 = 6, an = 3an - 1 can also be written as:

1) an = 6 ⋅ 3^n

2) an = 6 ⋅ 3^ (n + 1)

3) an = 2 ⋅ 3^n

4) an = 2 ⋅ 3^ (n + 1)

The correct choice is option 3) an = 2⋅3^n.

If we look at the initial sequence an = 3⋅an-1, and

a1 = 3⋅a0 = 6

a0 = 6/3

a0 = 2

We can now look at the sequence.

a0 = 2

a1 = 6

a2 = 18

a3 = 54

etc ...

A common factor in each of those numbers is 2, so we can rewrite the sequence by factoring out 2.

a0 = 2⋅1

a1 = 2⋅3

a2 = 2⋅9

a3 = 2⋅27

The numbers being multiplied by 2 are all factors of 3. So we can rewrite the sequence again as:

a0 = 2⋅3^0

a1 = 2⋅3^1

a2 = 2⋅3^2

a3 = 2⋅3^3

This sequence can now be rewritten as an = 2⋅3^n.