Question

if the 19th term of anAP is equal to the three of its sixth term if the 9th term is 19then find the first three terms of an AP

Answer 1

a (19)=3a (6)
a+18d=3 [a+5d]
a+18d=3a+15d
-2a=-3d
a=3/2d.........(i)

a (9)=19
a+8d=19
3/2d+8d=19
19d=38
D=2
From i equation. ..we get....
a=3/2×2
a=3.....
So the first three terms are.....3,5,7

Answer 2

As Given
A19=3A6
a+18d=3(a+5d)
a+18d=3a+15d
2a-3d=0
Also given that
A9=19
a+8d=19
a=19-8d
putting this value of a into 2a-3d=0 we get d=2 so a will be 3
so the first three terms of AP are 3, 5, 7