the following is an a.p 9 x y z 25 find the
solves
answers
In A.P
a1 is first term
d is common difference
a1 = 9
a5 = 25
Since:
a5 = a1 + 4 d
25 = 9 + 4 d
Subtract 9 to both sides
16 = 4 d
4 d = 16
Divide both sides by 4
d = 4
x = a2 = a1 + d = 9 + 4 = 13
y = a3 = a1 + 2d = 9 + 8 = 17
z = a4 = a1 + 3d = 9 + 12 = 21
To find the common difference in the arithmetic progression (AP) represented by the given sequence 9, x, y, z, 25, we need to look for a consistent pattern or relationship between the terms.
In an arithmetic progression, each term is obtained by adding a fixed value, called the common difference (d), to the previous term.
So, to find the common difference, we can find the difference between any two consecutive terms in the sequence. Let's find the differences between the terms:
x - 9
y - x
z - y
25 - z
Since the sequence is an arithmetic progression, all these differences should be equal. Let's set them equal to each other:
x - 9 = y - x = z - y = 25 - z
Now, we can proceed to solve these equations to find the values of x, y, and z.
1) x - 9 = y - x
Simplifying, we get:
2x = y + 9
2) y - x = z - y
Simplifying, we get:
2y = x + z
3) z - y = 25 - z
Simplifying, we get:
2z = y + 25
Now, we have a system of three equations with three variables (x, y, and z). We can solve this system simultaneously to find the values of x, y, and z.