The following of an AP is 9,x,y,z,25
1.Find the value of x,y,z
2.60 term
3.The next three terms after 25above.
To find the values of x, y, and z, we need to observe the pattern in the given arithmetic progression (AP) sequence.
From the given sequence, we see that the common difference is the same between consecutive terms.
Based on the given sequence, we can deduce the following:
The first term (a) is 9.
The common difference (d) is (x - 9) = (y - x) = (z - y).
The fifth term is 25.
Using the formula for the nth term of an arithmetic progression (AP), we can set up equations to solve for x, y, and z:
5th term (a + 4d) = 25
9 + 4(x - 9) = 25
4x - 27 = 25
4x = 25 + 27
4x = 52
x = 13
Now that we have the value of x, we can find the common difference (d):
Common difference = x - 9
d = 13 - 9
d = 4
Using the values of x and d, we can find the values of y and z:
y = x + d
y = 13 + 4
y = 17
z = y + d
z = 17 + 4
z = 21
Therefore, the values of x, y, and z are x = 13, y = 17, and z = 21.
To find the 60th term, we can use the formula for the nth term of an AP:
60th term = a + (n - 1)d
60th term = 9 + (60 - 1)4
60th term = 9 + 59*4
60th term = 9 + 236
60th term = 245
Therefore, the 60th term of the given AP is 245.
To find the next three terms after 25, we can use the previous common difference of 4:
26th term = 25 + (26 - 1)4
26th term = 25 + 25*4
26th term = 25 + 100
26th term = 125
27th term = 26th term + 4
27th term = 125 + 4
27th term = 129
28th term = 27th term + 4
28th term = 129 + 4
28th term = 133
Therefore, the next three terms after 25 in the given AP are 125, 129, and 133.
To find the values of x, y, and z in the arithmetic progression 9, x, y, z, 25, we need to identify the common difference first.
The common difference (d) can be found by subtracting the preceding term from the succeeding term. In this case, the preceding term is 9 and the succeeding term is x. So, the common difference can be represented as x - 9.
1. Find the value of x, y, z:
To find the common difference, we compare the difference between each pair of consecutive terms in the given sequence.
The difference between the first two terms (9 and x) is x - 9.
The difference between the second and third terms (x and y) is y - x.
The difference between the third and fourth terms (y and z) is z - y.
The difference between the fourth and fifth terms (z and 25) is 25 - z.
Since it is an arithmetic progression, all of these differences should be the same. Therefore, equating them, we get:
x - 9 = y - x = z - y = 25 - z
Simplifying these equations, we can find the values of x, y, and z:
From the first equation, x - 9 = y - x:
2x = 9 + y
From the second equation, y - x = z - y:
2y = x + z
From the third equation, z - y = 25 - z:
2z = y + 25
Substituting the value of y from the third equation into the second equation:
2y = (2z - 25) + z
2y = 3z - 25
Substituting the value of x from the first equation into the second equation:
2x = 9 + (2y - x)
3x = 9 + 2y
Solving these equations simultaneously, we can find the values of x, y, and z. However, we need additional information or more equations to determine the values explicitly.
2. 60th term:
To find the 60th term of an arithmetic progression, we need the first term (a) and the common difference (d).
In this case, the first term (a) is 9, and we still need to find the common difference (d) to calculate the 60th term.
3. The next three terms after 25:
To find the next three terms after 25 in the arithmetic progression, we also need the common difference (d).
Without the explicit value of the common difference, we cannot determine the 60th term or the next three terms after 25.