Question

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

Answer 1

Answer:

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.............

Step-by-step explanation:

Answer 2

Step-by-step explanation:

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

a+18d=3a+15d

18d-15d=2a

3d=2a............=a=3d/2

now

a+8d=19(putting value of A)

3d/2+8d=19

3d+16d=38

19d=38

d=2 ...

so on a =3*2/2

a=3

you make so with formula