the third term

Question

the third term of a geometric sequence is 6 and the fifth is 81 times the first term. write the first five terms of the progression, assuming the terms are positive

Answer 1

nth term in geometric sequence= a1*r^(n-1)

So,

a1*r^2=6

a1r^4=81

Solving the above

r=3sqrt(3/2)

a1=4/9

So the first five terms are

 

4/9,(4/3)*sqrt(3/2),6,18*sqrt(3/2),81