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

1 Answer
Oct 16, 2017

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