Consider the sequence

Question

The recursive Function is ___41,29,17,5____ with A_1

=_____.

A
n
=
12
A
n
−
1
A
n
​
=12A
n−1
​

,
−
12
−12

A
n
=
A
n
−
1
−
12
A
n
​
=A
n−1
​
−12
, 41

A
n
=
A
n
−
1
+
12
A
n
​
=A
n−1
​
+12
, 53

Answer 1

To determine the recursive function and the first term $A_1$ of the sequence $41,29,17,5$, we can analyze the differences between consecutive terms.

• The difference between 41 and 29 is $41-29=12$
• The difference between 29 and 17 is $29-17=12$
• The difference between 17 and 5 is $17-5=12$

It seems that each term in the sequence decreases by 12. This suggests that the recursive relation is:

$$A_n=A_{n-1}-12$$

Now, let's find the first term $A_1$.

From the given sequence:

• For $n=4$: $A_4=5$
• For $n=3$: $A_3=A_4+12=5+12=17$
• For $n=2$: $A_2=A_3+12=17+12=29$
• For $n=1$: $A_1=A_2+12=29+12=41$

Based on this analysis:

The recursive function is: $$A_n=A_{n-1}-12$$

with $A_1=41$.