Question

if for a g.p. t3= 1/3,t6=1/81 find a​

Answer 1

Answer:

Given : t3 = 1/3

t6 = 1/81

To find: a

Solution:

For a G.P. ,

t3 = 1/3 ..............(given)......(1)

t6 = 1/81 ...........( given).......(2)

We know that ,

tn = ar^n-1

Simplifying (1), we get

t3 = ar^ 3-1

ar²= 1/3 ...........(3)

Simplifying (2), we get

t6 = ar^ 6-1

ar⁵ = 1/81.........(4)

Dividing equation (1 ) and (2), we get

ar²/ ar⁵= 1/3 / 1/81

1/r³= 27

r³= 1/27

r=1/3

Substituting the value of r in (1) , we get

a( 1/3)²= 1/3

1/9a = 1/3

a = 1/3 / 1/9

a= 3