Use patterns or a linear equation to complete the table.
P 2 88 8 10 ?
Q 22 ? 110 110 330
To complete the table using patterns or a linear equation, we need to identify the relationship between the numbers in each row.
Let's analyze each row separately:
For Row P:
Looking at the numbers in Row P (2, 88, 8, 10), it isn't immediately evident what the pattern is. However, we can try to find a linear equation:
Let's call the position of each number in Row P as n.
n = 1: P(1) = 2
n = 2: P(2) = 88
n = 3: P(3) = 8
n = 4: P(4) = 10
Based on the given information, we can try to find a pattern using a linear equation of the form P(n) = an + b.
Using the first two points (n = 1 and n = 2), we can create two equations:
2 = a(1) + b ---- Equation 1
88 = a(2) + b ---- Equation 2
Solving these equations simultaneously, we subtract Equation 1 from Equation 2:
(88 - 2) = a(2 - 1) + b - (a(1) + b)
86 = a + a(1 - 1)
86 = a
Now that we have the value of a, we can substitute it into one of the equations to find b:
2 = (86)(1) + b
2 = 86 + b
b = 2 - 86
b = -84
Therefore, the linear equation representing the pattern in Row P is P(n) = 86n - 84.
Now we can use this equation to find the missing value in Row P:
n = 5: P(5) = 86(5) - 84 = 430 - 84 = 346
So the missing value in Row P is 346.
For Row Q:
Looking at the numbers in Row Q (22, ?, 110, 110, 330), it is clear that each number is simply multiplied by the corresponding position in the row.
n = 1: Q(1) = 22 * 1 = 22
n = 2: Q(2) = 22 * 2 = 44
n = 3: Q(3) = 22 * 3 = 66
n = 4: Q(4) = 22 * 4 = 88
Using this pattern, we can determine the missing value in Row Q:
n = 2: Q(2) = 22 * 2 = 44
So the missing value in Row Q is 44.
To summarize, the completed table is:
P 2 88 8 10 346
Q 22 44 110 110 330