Question

(tn)is an a.p.such that t4/t7=2/3.find t8/t9

Answer 1

T4/T7 =2/3. =a+3d/a+6d=2/3 =3a+9d=2a+12d =3a-2a=12d-9d ;a=3d putting value of a= 3d in T8/T9=a+7d/a+8d=3d+7d /3d+8d=10d/11d= 10/11. T8/T9=10/11

Answer 2

Answer:

$\frac{t_8}{t_9}=\frac{10}{11}$

Step-by-step explanation:

Formula of nth term = $a_n=a+(n-1)d$

$t_4=a+(4-1)d=a+3d$

$t_7=a+(7-1)d=a+6d$

$\frac{t_4}{t_7}=\frac{2}{3}$

$\frac{a+3d}{a+6d}=\frac{2}{3}$

$=3a+9d=2a+12d$

$=3a-2a=12d-9d$

a=3d

putting value of a= 3d in

$\frac{t_8}{t_9}=\frac{a+7d}{a+8d}$

$=\frac{3d+7d}{3d+8d}$

$=\frac{10d}{11d}$

=$\frac{10}{11}$

$\frac{t_8}{t_9}=\frac{10}{11}$

Hence $\frac{t_8}{t_9}=\frac{10}{11}$