Given the sequence 2, 6, 18, 54, ..., which expression shown would give the fifteenth term?
2¹⁵, 2·3¹⁵, 2·3¹⁴

Solution:

Given, the series is in geometric progression

First term, a₁ = 2

Common ratio, r = 6/2 = 3

r = 3

We have to find the fifteenth term of the sequence.

Geometric progression can be represented by the formula,

\(f(n) = a_{1}(r)^{n-1}\)

So, \(a_{15} = (2)(3)^{15-1}\)

\(a_{15} = (2)(3)^{14}\)

Therefore, the expression is \(a_{15} = (2)(3)^{14}\).

Given the sequence 2, 6, 18, 54, ..., which expression shown would give the fifteenth term?

Summary:

Given the sequence 2, 6, 18, 54, ...,the expression that would give the fifteenth term is \(a_{15} = (2)(3)^{14}\).