Question

The following of an AP 9,X,Y,Z,25
find the value of X,Y,Z
The 60 term

Answer 1

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 \( 245 \).