Question

the 19th term of an A.P is equal to three times its sixth term.If its 9th term is 19 find A.P

Answer 1

t19=3*t6
a+18d=3(a+5d)
a+18d=3a+15d
18d-15d=3a-a
3d=2a
3/2=a/d
let the common multiple be x.
a=3x&d=2x
t9=19............(given)
a+8d=19
3x+8(2x)=19
3x+16x=19
19x=19
x=19/19
x=1
a=3x=3(1)=3
d=2x=2(1)=2
a=3,d=2
t1=a
t1=3,
t2=a+d=3+2=5......
Therefore we get AP
3,5,7.............