HELLO,

Let the AP is \(a_1, a_2, a_3,...a_n\) with common difference d.

Given in the question,

\(a_5 + a_9= 30\)

\(a_1+4d+a_1+8d=30\)

\(2a_1+12d=30\)

\(a_1+6d=15\) ------------- 1

Now again given in the question,

\(a_{25}=3a_8\)

\(a_1+24d= 3(a_1+7d)\)

\(a_1+24d= 3a_1+21d
\)

\(2a_1-3d=0\) -------------- 2

Now solving equation 1 and 2 we get ( \(2* eqn 1 - eqn2\)),

\(15d=30\)

d=2 and \(a_1=3\)

hence, \(a_1=3, a_2= 3+2, a_3= 3+2+2 ...\)

**So, the required AP is 3,5,7,9 ...**

**I HOPE YOU WILL UNDERSTAND.**