Find the next three terms of the sequence 3, 9, 27, 81, . . .

Solution:

Given,

The sequence 3, 9, 27, 81, . . .

This is a geometric sequence since there is a common ratio between each of them.

In this case, multiplying the previous term in the sequence by 3 gives the next term.

A_n = a₁ r^{n - 1}.

Where, r = 3, a₁ = 3.

Form of geometric sequence = a₁ r^{n - 1}.

Substituting , we get,

a₅ = 3(3)^{5 - 1}

= 3(3)⁴

= 3(81)

= 243

a₆ = 3 (3)^{6 - 1}

= 3(3)⁵

= 3(243)

= 729

a₇ = 3 (3)^{7 - 1}

= 3(3)⁶

= 3(729)

= 2187

Therefore, the next three terms are 243, 729 and 2187.

Find the next three terms of the sequence 3, 9, 27, 81, . . .

Summary:

The next three terms of the sequence 3, 9, 27, 81, . . . are243, 729 and 2187.