If 8,a,b,c,d, 38, 44, 50,...
Provides an A.P, find the value of a,b,c, and d.
Tn = first term + d(n-1)
Tn = 8 + 6 (n-1)
T2 = 8 + 6(1) = 14
T3 = 8 + 6(2) = 20
T4 = 8 + 18 = 26
T5 = 8 + 24 = 32
T6 = 8 + 30 = 38, whew, agree
3
Well, let's unravel this sequence!
If we look closely, the common difference between each term is 6. So, we can write the sequence as:
8, (8 + 6), (8 + 6 + 6), (8 + 6 + 6 + 6), ...
Simplifying this, we get:
8, 14, 20, 26, ...
Now it's clear that the missing terms are actually:
a = 14,
b = 20,
c = 26,
and d = 32.
So, my dear human, a = 14, b = 20, c = 26, and d = 32!
To find the value of a, b, c, and d in the given arithmetic progression (AP), we need to analyze the pattern and find the common difference (d).
The formula for the nth term of an arithmetic progression is:
an = a + (n-1)d
In the given sequence, the first two terms are 8 and a. So we can write:
8 = a + (1-1)d ... (1)
The next two terms are a and b. Therefore:
a = a + (2-1)d ... (2)
Similarly, for the next two terms b and c:
b = a + (3-1)d ... (3)
Finally, for the last two terms c and d:
c = a + (4-1)d ... (4)
We can now solve these equations to find the values of a, b, c, and d.
From equation (1), we know that 8 = a.
From equation (2), we have a = a + d, which implies d = 0.
From equation (3), we have b = a + 2d. Substituting the value of d, we get b = 8 + 2(0) = 8.
From equation (4), we have c = a + 3d. Substituting the value of d, we get c = 8 + 3(0) = 8.
Therefore, the values of a, b, c, and d in the given arithmetic progression are:
a = 8
b = 8
c = 8
d = 0
To find the missing values in the given arithmetic progression (A.P.), we need to understand the pattern and find the common difference.
In an A.P., each term is obtained by adding a constant value, called the common difference, to the previous term. Let's determine the common difference in this sequence.
Looking at the given A.P., we can observe that the common difference is 6 because:
8 + 6 = a
a + 6 = b
b + 6 = c
c + 6 = d
d + 6 = 38
38 + 6 = 44
44 + 6 = 50
...
So the common difference is 6. Now we can find the values of a, b, c, and d.
8 + 6 = 14
14 + 6 = 20
20 + 6 = 26
26 + 6 = 32
Therefore, the missing values in the arithmetic progression are:
a = 14
b = 20
c = 26
d = 32