Question

The product of 3rd and 8th term of a G.P is 243. If its 4th term is 3, find its 7th term

Answer 1

Therefore 7th term of the G.P is 81

Step-by-step explanation:

Given that ,

The product of third term and eighth term is 243

The  forth term is 3.

Let the first term of the G.p be a

And common ratio be r

Then nth term of the g.p is $T_n=ar^{n-1}$

Then $T_4=ar^{4-1}=ar^3$ =3.....(1)

$T_3=ar^2$

$T_8= ar^7$

$T_7=ar^6$

Therefore ,

$T_3.T_8=ar^2.ar^7= a^2r^9=243$....(2)

The equation (2) divides by (1)

$\frac{a^2r^9}{ar^3}=\frac{243}{3}$

$\Rightarrow ar^6=81$      [In case of division, power of the same base gets subtract ]

$\Rightarrow T_7=81$

Therefore 7th term of the G.P is 81