Find the values of A and Q in the AP _ 12 ,Q,18
q - p = d
18 - q = d
p + 12 = d
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so q = 18-d and p = d - 12
so (18-d) - ( d-12) = d
30 - 2 d = d
d = 10
q = 18 - 10 = 8
p = 8 -10 = -2
so
-12 , -2 , 8 , 18
(yuh)
Thank you Ariana Grande!
Im glad i could help!
To find the values of A and Q in the arithmetic progression (AP) represented by 12, Q, 18, we can use the formula for an arithmetic progression:
An = A + (n - 1) × d
where:
- An is the nth term of the arithmetic progression,
- A is the first term of the arithmetic progression,
- n is the position of the term in the sequence,
- d is the common difference between consecutive terms.
In this case, the first term A is 12, the second term Q is unknown, and the third term is 18. We can assume that the common difference d is the same between all the terms.
To find the common difference d, we can subtract any term from its previous term:
d = 18 - 12 = 6
Now that we know the common difference, we can substitute it into the formula to find the value of Q. Since Q is the second term (n = 2), we use n = 2 in the formula:
Q = A + (2 - 1) × d
Q = 12 + (1) × 6
Q = 12 + 6
Q = 18
Therefore, the value of Q in the arithmetic progression 12, Q, 18 is 18.