Question
Which recursive formula can be used to define this sequence for n>1? 9, 15, 21, 27, 33, 39, ...
Answers
GPT-4o mini
To find a recursive formula for the sequence given (9, 15, 21, 27, 33, 39, ...), we first need to determine how the sequence progresses from one term to the next.
Looking at the differences between consecutive terms:
- 15 - 9 = 6
- 21 - 15 = 6
- 27 - 21 = 6
- 33 - 27 = 6
- 39 - 33 = 6
The difference between each consecutive term is consistently 6. Thus, we can express the recursive formula as:
\( a_n = a_{n-1} + 6 \)
for \( n > 1 \), where \( a_1 = 9 \).
So, the complete recursive definition of the sequence is:
- \( a_1 = 9 \)
- \( a_n = a_{n-1} + 6 \) for \( n > 1 \)
Looking at the differences between consecutive terms:
- 15 - 9 = 6
- 21 - 15 = 6
- 27 - 21 = 6
- 33 - 27 = 6
- 39 - 33 = 6
The difference between each consecutive term is consistently 6. Thus, we can express the recursive formula as:
\( a_n = a_{n-1} + 6 \)
for \( n > 1 \), where \( a_1 = 9 \).
So, the complete recursive definition of the sequence is:
- \( a_1 = 9 \)
- \( a_n = a_{n-1} + 6 \) for \( n > 1 \)