Question

9th term of ap is 19 . 19th term of ap is equal to 3 tines the 6th term

Answer 1

9th term is = a + (9-1) d=> 19= a+8d .. eq.1
19th term is 3 times 6th term so 3{a +(6-1)d}= a+ (19-1)d => 3a+ 15d = a+18d => 3a-a=18d-15d => 2a=3d so a = 3/2d
Putting this in eq1 so
3/2d +8d = 19
(3d + 16d)/2 = 19
19d= 19x2
19d = 38
D= 2
So d = 2 then putting this in eq1 19=a+8d
19= a + 8x2
19= a + 16
19-16=a
a= 3 now by a=3 and d = 2 u can find any term

Answer 2

19=a+8d                                              (equation 1)

a+18d=3(a+5d)

a+18d=3a+15d

3a-a=18d-15d

2a=3d

a=3d/2   (substitute in equation 1)

19=3d/2+8d

19=3d/2+16d/2     (transpose 2 to other side)

19*2=19d

38=19d

d=38/19

d=2

a=3d/2

a=3*2/2

a=3