Question

if 6,P,q, and 18 are in an arithmetic sequence find the value of P and Q

Answer 1

6 --- P --- Q --- 18
those three gaps are the same
18 - 6 =12
12/3 = 4
so each gap is 4 units
sp
6 10 14 18

Answer 2

To find the values of P and Q in the arithmetic sequence, we need to determine the common difference between the terms.

In an arithmetic sequence, the difference between any two consecutive terms is constant.

Given: 6,P,Q,18

Let's set up two equations based on the given information:

1. P - 6 = Q - P
2. 18 - Q = Q - P

Simplify these equations:

1. P - 6 = Q - P
2P = Q + 6
2P - Q = 6

2. 18 - Q = Q - P
18 + P = 2Q
P = 2Q - 18

Now set the two equations equal to each other:

2P - Q = 6
2(2Q - 18) - Q = 6
4Q - 36 - Q = 6
3Q - 36 = 6
3Q = 42
Q = 14

Now that we have found the value of Q, substitute it back into the equation to find P:

P = 2Q - 18
P = 2(14) - 18
P = 28 - 18
P = 10

Therefore, the values of P and Q in the arithmetic sequence are P = 10 and Q = 14.

Answer 3

Yes, you are correct. I apologize for the mistake in my previous calculation.

Given that the common difference between the terms in the arithmetic sequence is 4, we can determine the values of P and Q as follows:

6 + 4 = 10 (P)
10 + 4 = 14 (Q)
14 + 4 = 18

So, the correct values in the arithmetic sequence are P = 10 and Q = 14. Thank you for pointing out the correct calculation.