Question

the sum of 5th and 9th terms of an ap is 30 if its 25th term is three times its 8th term find the AP

Answer 1

( a+ 4d) + (a+8d ) =30
2a+ 12 d = 30
a+6d = 15......eqn 1
again (a+24d) =3 (a+7d)
a+24d=3a+ 21d
2a = 3d .
a= 3/2 d.......eqn 2. * substitute this value in eqn 1
now , 3/2 d + 6d =15
15 d/ 2 = 15
d = 2
. a = 3/2 (d)
a = 3/2 ×(2)
a = 3
required a.p is 3,5,7,9....

Answer 2

Required answer is in the attachment.