finish the sequence 3, 8, 13, 18, 23 __,___,___
and write me a recursive function
tell me the constant difference
the explict function
To finish the sequence 3, 8, 13, 18, 23, we can observe that the numbers are increasing by 5 each time. So, to find the next three terms, we can add 5 to the last number multiple times:
3 + 5 = 8
8 + 5 = 13
13 + 5 = 18
Therefore, the next three terms are 28, 33, and 38. Hence, the complete sequence is:
3, 8, 13, 18, 23, 28, 33, 38
Now, let's write a recursive function in Python to calculate the nth term of this sequence:
```python
def recursive_sequence(n):
if n == 1:
return 3
else:
return recursive_sequence(n-1) + 5
```
In this function, we're using recursion to calculate the nth term. If n is equal to 1, we return the first term of the sequence which is 3. Otherwise, we call the recursive_sequence function with n-1 and add 5 to the result.
The constant difference in this sequence is 5. From one term to the next, we always add 5 to get the next number.
To express the sequence as an explicit function, we can use the formula:
nth term = initial term + (n - 1) * difference
In our case, the initial term is 3 and the difference is 5. So, the explicit function for this sequence is:
nth term = 3 + (n - 1) * 5