Question

an=an-1+___

What number belongs in the blank space of the recursive formula
6
12
4
2

Answer 1

To determine the number that belongs in the blank space of the recursive formula \( a_n = a_{n-1} + \_\_\_ \), we can look at the sequence provided: 6, 12, 4, and 2.

1. Let's analyze the sequence:
- The change from 6 to 12 is an increase of 6.
- The change from 12 to 4 is a decrease of 8.
- The change from 4 to 2 is a decrease of 2.

2. Given these changes, it seems that the sequence is neither arithmetic nor constant. However, if we consider each transition:
- From the first term (6) to the second term (12), we added 6.
- And if we assume that the pattern continues for the next value:
- Let’s rewrite the sequence in terms of the recursive formula:

For the first term:
\[ a_1 = 6 \]

For the second term:
\[ a_2 = a_1 + 6 \]

For the third term:
\[ a_3 = a_2 - 8 \]

For the fourth term:
\[ a_4 = a_3 - 2 \]

3. Based on this, the choice of 6 seems to be the most logical for the first transition, as it provides a point of recursion.

Thus, the number that can be logically placed in the blank for the recursive formula \( a_n = a_{n-1} + \_\_\_ \) concerning these observations is:

**6**