THE NUMBERS 11,P, Q,21.5,...FORM AN LINEAR SEQUENCE.FIND THE VALUE OF P AND Q
three steps (differences) from 11 to 21.5
11 + 3 d = 21.5 ... d = 3.5
P = 11 + d
Q = 11 + 2 d
3d = 21.5 - 11
find d, then use it.
a = 11
a + 3d = 21.5
3d = 21.5 - 11 = 10.5
d = 3.5
p = 11 + d = 14.5
q = 11 + 2d = 18
THANKS
To find the values of P and Q in the linear sequence, we need to analyze the given sequence and identify the pattern.
The sequence given is 11, P, Q, 21.5, ...
To determine the pattern, let's calculate the common difference (d) between consecutive terms:
Term 2 - Term 1: P - 11
Term 3 - Term 2: Q - P
Term 4 - Term 3: 21.5 - Q
This means that P - 11 = Q - P = 21.5 - Q
To solve this system of equations, we can start by finding two equations from the given information:
P - 11 = Q - P (Equation 1)
Q - P = 21.5 - Q (Equation 2)
We can simplify Equation 2 by rearranging it:
2Q - P = 21.5
Now, we can solve the system of equations. We can choose any approach, but let's use the method of substitution:
From Equation 1, we get:
P = Q - P + 11
Substitute this value of P into Equation 2:
2Q - (Q - P + 11) = 21.5
Simplifying the equation:
Q - P = 21.5 + Q - 11
Q - P = 10.5 + Q
We can cancel out the Q's on both sides:
- P = 10.5
Multiply both sides by -1:
P = -10.5
Now, substitute this value of P into Equation 1:
-10.5 = Q + 10.5
Move 10.5 to the other side:
Q = -10.5 - 10.5
Q = -21
Therefore, the value of P is -10.5 and the value of Q is -21.