Question

Ans please someon
Mathematics​

Answer 1

Answer:

i know the answer for the first one ok? just to help

Step-by-step explanation:

5th term =a+4d                                 formula(nth term of AP=a+(n-1)d)

9th term=a+8d

sum=a+4d+a+8d=30

2a+12d=30

2(a+6d)=30

a+6d=15------------------(1)

now solving the second part:

25th term =3 times 8th term

a+24d=3(a+7d)

a+24d=3a+21d

3d=2a

d=2a/3---------------------(2)

substituting value of d in 1 we get,

a+6(2a/3)=15

a+4a=15

5a=15

a=3

by substituting a in 2 we get,

d=6/3

d=2

so the AP is 3,5,7,9.....

mark as brainliest if you are satisfied with my answer

Answer 2

SOLUTION :

$1) \: 5th \: term \: of \: an \: ap = a + 4d \\ \\ 9th \: term \: of \: an \: ap \: = a + 8d \\ \\ given \: sum \: of \: the \: terms \: = 30 \\ \\ = >2a \: + 12d = 30 - eq(1)\\ \\ 8th \: term \: of \: an \: ap \: = a + 7d \\ \\ 25th \: term \: of \: an \: ap = a + 24d \\ \\ relation \: between \: 8th \: and \: 25th \: term \: is \\ \\ \: a + 24d = 3(a + 7d) \\ \\ = > a + 24d = 3a + 21d \\ \\ = > 3d = 2a \: \\ \\ = > 2a - 3d = 0 - eq(2) \\ \\ subtracting \: eq(1) \: and \: eq(2) \\ \\ = > 2a + 12d = 30 \\ \: \: \: \: \: \: \: \: \: \: \: 2a - 3d = 0 \\ \: \: \: \: \: \: \: ( - ) \: \: \: \: \: ( + ) \\ - - - - - - - - - \\ \\ = > 12d + 3d = 30 - 0 \\ \\ = > 15d = 30 \\ \\ = > d = 2 \\ \\ from \: eq(1) \: \\ \\ 2a + 12(2) = 30 \\ \\ = > 2a = 6 \\ \\ = > a = 3 \\ \\ first \: term(a) = 3 \\ \\ 2nd \: term \: = (a + d) = 3 + 2 = 5 \\ \\ 3rd \: term = (a + 2d) = 7 \\ \\ 4th \: term \: = (a + 3d) = 9 \\ \\ 5th \: term \: = (a + 4d) = 11$

∴THE SEQUENCE IS 3 ,5 , 7,

9 ,....

HOPE IT HELPS !!!!