In an arithmetic progression (AP), the difference between consecutive terms is constant. Let's denote the first term as \( a \) and the common difference as \( d \).
From the given sequence:
- The first term \( a = 9 \)
- The fifth term is \( 25 \)
We can find the common difference \( d \) using the formula for the \( n \)-th term of an AP, which is given by:
\[ a_n = a + (n - 1) d \]
For the fifth term \( a_5 \):
\[ a_5 = a + 4d = 25 \]
Substituting \( a = 9 \):
\[ 9 + 4d = 25 \]
Now, solve for \( d \):
\[ 4d = 25 - 9 \] \[ 4d = 16 \] \[ d = 4 \]
Now that we have the common difference \( d \), we can find the values of \( X \), \( Y \), and \( Z \):
- Second term (\( X \)):
\[ X = a + d = 9 + 4 = 13 \]
- Third term (\( Y \)):
\[ Y = a + 2d = 9 + 2 \cdot 4 = 9 + 8 = 17 \]
- Fourth term (\( Z \)):
\[ Z = a + 3d = 9 + 3 \cdot 4 = 9 + 12 = 21 \]
Thus, the values are:
- \( X = 13 \)
- \( Y = 17 \)
- \( Z = 21 \)
Now, we can find the 60th term of the AP:
\[ a_{60} = a + (60 - 1)d = 9 + 59 \cdot 4 \] \[ a_{60} = 9 + 236 = 245 \]
So, the values are:
- \( X = 13 \)
- \( Y = 17 \)
- \( Z = 21 \)
- The 60th term is \( 245 \).
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