Question: Which recursive equation represents the pattern? 1 answer below »
n an
1 1
2 6
3 12
4 19
Which recursive equation represents the pattern?
an = an – 1 + 3n + 1
an = an – 1 + 3(n + 1)
an = an – 1 + (n+3)
an = an – 1 + (n-3)
My answer is the 2nd one.
well,
a2 added 5
a3 added 6
a4 added 7
so, what do you think?
Steve, to be honest with you I'm a little lost.I'mm71 years old and trying to help my grandson.
The correct recursive equation for the given pattern is the third one: an = an – 1 + (n+3).
To determine which recursive equation represents the given pattern, we need to understand the pattern itself. Looking at the pattern in the table, we can see that the values in the second column are increasing as n increases.
Now let's analyze the options:
1. an = an – 1 + 3n + 1 - This equation includes the term 3n, which means the values in the second column should increase by 3 times n in each step. However, this contradicts the pattern where the values are not increasing by 3 times n.
2. an = an – 1 + 3(n + 1) - In this equation, the values in the second column increase by 3 times (n + 1). This matches the pattern, as the values are indeed increasing by this amount in each step. Therefore, this equation could represent the pattern.
3. an = an – 1 + (n+3) - This equation includes the term (n + 3), which means the values in the second column should increase by n + 3 in each step. However, this contradicts the pattern where the values are not increasing by n + 3.
4. an = an – 1 + (n-3) - This equation includes the term (n - 3), which means the values in the second column should increase by n - 3 in each step. However, this contradicts the pattern, as the values are not increasing by n - 3.
Based on this analysis, it seems that your answer is correct. The second recursive equation, "an = an – 1 + 3(n + 1)", represents the given pattern.