Answer:
The 3rd sequence could not be described by the following recursive definition tn+1 = tn + 6
Explanation:
* Lets revise the recursive formula
1. Determine if the sequence is arithmetic (Do you add, or subtract, the
same amount from one term to the next?)
2. Find the common difference. (The number you add or subtract.)
3. Create a recursive formula by stating the first term, and then stating
the formula to be the previous term plus the common difference.
a1 = first term;
an+1= an + d
- Where:
# a1 = the first term in the sequence
# an = the nth term in the sequence
# an+1 = the term after the nth term
# n = the term number
# d = the common difference.
* Now lets solve the problem
∵ tn+1 = tn + 6
∴ d = 6 ⇒ common difference
- The 1st sequence 5 , 11 , 17 , 23 , 29 , .... has common difference 6
- The 2nd sequence 0 , 6 , 12 , 18 , 24 , .... has common difference 6
- The 3rd sequence 6 , 9 , 12 , 15 , 18 , .... has common difference 3
∴ This sequence could not be described by the following recursive
definition tn+1 = tn + 6
* The 3rd sequence could not be described by the following recursive
definition tn+1 = tn + 6