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.
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.
1 answer