If 8,A,B,C,D,38,44,50 provide AP. find the values of A,B,C and D
5d = 38-8
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answer
To find the values of A, B, C, and D in the arithmetic progression (AP) 8, A, B, C, D, 38, 44, 50, we need to analyze the pattern and use the properties of an AP.
In an AP, the difference between any two consecutive terms is constant. To determine this common difference, we can analyze the differences between adjacent terms in the given sequence.
First, let's find the difference between each pair of consecutive terms:
Difference between the first and second term: A - 8
Difference between the second and third term: B - A
Difference between the third and fourth term: C - B
Difference between the fourth and fifth term: D - C
Difference between the fifth and sixth term: 38 - D
Difference between the sixth and seventh term: 44 - 38
Difference between the seventh and eighth term: 50 - 44
Since it is an AP, all these differences should be equal.
From the given sequence, we can see that the differences between consecutive terms are as follows:
A - 8 = B - A = C - B = D - C = 38 - D = 44 - 38 = 50 - 44
Now, let's simplify these equations step-by-step to find the values of A, B, C, and D.
A - 8 = B - A (Equation 1)
B - A = C - B (Equation 2)
C - B = D - C (Equation 3)
D - C = 38 - D (Equation 4)
38 - D = 44 - 38 (Equation 5)
44 - 38 = 50 - 44 (Equation 6)
Simplifying Equation 1:
2A = B + 8
Simplifying Equation 2:
2B = A + C
Simplifying Equation 3:
2C = B + D
Simplifying Equation 4:
2D = C + 38
Simplifying Equation 5:
2D = 76
From Equation 5, we get D = 38.
Substituting D = 38 into Equation 4, we get:
2 * 38 = C + 38
C = 38
Substituting C = 38 into Equation 2, we get:
2B = A + 38
Substituting D = 38 into Equation 3, we get:
2C = B + 38
2 * 38 = B + 38
B = 38
Substituting B = 38 into Equation 2, we get:
2 * 38 = A + 38
A = 38
Therefore, the values of A, B, C, and D in the given arithmetic progression are:
A = 38
B = 38
C = 38
D = 38
If 8,a,b,c,d,38,44,50.....
Provides an A.P,find the value of a,b,c and d