Two terms in a geometric sequence are a3=729 and a4=243.

What is the first term of the sequence, and what is the recursive rule that describes the sequence?

Step-by-step explanation:

Let the first term = a and common difference = d

Given,

= 729 and = 243

To find, the first term of the given sequence (a) = ?

We know that,

The nth term of a G.P.

The 3rd term of a G.P.

⇒ = 729          ..............(1)

The 4th term of a G.P.

⇒ = 243          ..............(2)

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

=

⇒

Put in equation (1), we get

= 729    

⇒ = 729    

⇒ a = 9 × 729 = 6561

∴ The first term of the given sequence (a) = 6561