Question

How do you write the first five terms of the sequence defined recursively `a_1=3, a_(k+1)=2(a_k-1)`?

Answer 1

3, 4, 6, 10, 18

Explanation:

When a sequence is defined recursively, the previous term is used to find the next term. Start by using `a_1` to find `a_2` (second term).

Substitute `a_1` for `a_k`.
`a_(1+1)=2(a_1-1)`
`a_2=2(a_1-1)`
Because `a_1=3`, substitute `a_1` for `3` to find `a_2`.
`a_2=2(3-1)`
`a_2=2(2)`
`a_2=4` This is your second term!

Now use `a_2` to find `a_3` just like how you used `a_1` to find `a_2`.
`a_(2+1)=2(a_2-1)`
`a_3=2(4-1)`
`a_3=2(3)`
`a_3=6` This is your third term!

Repeat these steps to find `a_4` using `a_3`.
`a_(3+1)=2(a_3-1)`
`a_4=2(6-1)`
`a_4=2(5)`
`a_4=10` This is your fourth term!

Find `a_5` using `a_4`.
`a_(4+1)=2(a_4-1)`
`a_5=2(10-1)`
`a_5=2(9)`
`a_5=18` This is your fifth term!

List the terms from least to greatest and separate the terms with commas.

Answer: 3, 4, 6, 10, 18