If 8,A,B,C,D 38,44,50 provide an AP find the values of A,B,C and D
looking at the terms 38,44,50, it is clear that the common difference is 6. So, the AP goes
8,14,20,26,32,38,44,50, ...
Apologies for the confusion. You are correct in observing that the common difference between the terms 38, 44, and 50 is 6. Therefore, the arithmetic progression (AP) can be written as:
8, 14, 20, 26, 32, 38, 44, 50, ...
In this case, the values of A, B, C, and D would be 14, 20, 26, and 32, respectively.
To find the values of A, B, C, and D in the arithmetic progression (AP) 8, A, B, C, D, 38, 44, and 50, we need to observe the pattern and use the properties of an AP.
In an arithmetic progression, the difference between any two consecutive terms is constant. Let's find this common difference by subtracting each term from its previous term:
First pair: A - 8 = B - A = C - B = D - C
Second pair: 38 - D = 44 - 38 = 50 - 44
From the first pair, we get:
A - 8 = B - A = C - B = D - C
Re-arranging this equation, we get:
A - B = B - C = C - D
From the second pair, we get:
38 - D = 44 - 38 = 50 - 44
Simplifying this equation, we get:
- D = 6 = 6
Comparing this with the previous equation, we see that A - B = B - C = C - D = 6.
So, let's proceed by substituting D = 6 into the equation A - B = B - C:
A - B = B - C
8 - B = B - C (Substituting A = 8)
2B = 8 + C
2B = C + 8
Since A - B = B - C = C - D = 6, we can substitute 6 for A - B:
6 = C - D
6 = C - 6
C = 12
Substituting C = 12 into 2B = C + 8, we get:
2B = 12 + 8
2B = 20
B = 10
Now, substituting B = 10 into (2B = C + 8) and solving for C:
2(10) = C + 8
20 = C + 8
C = 20 - 8
C = 12
Lastly, let's find A. Substituting C = 12 into A - B = B - C, we get:
A - B = B - C
A - 10 = 10 - 12
A - 10 = -2
A = -2 + 10
A = 8
Therefore, the values of A, B, C, and D are 8, 10, 12, and 6, respectively.