Question

Recursive & Explicit Definitions
Consider the sequence:
2, 6, 18, 54, 162,

Determine the 15th term of the sequence.

9.565,938
3,188,646
2.430
28.597,814

Answer 1

Answer:

$T_{15} = 9565938$

Step-by-step explanation:

Given

Sequence: 2, 6, 18, 54, 162,

Required

Determine the 15th term

The above sequence is a geometric sequence. So, first, we calculate the common ratio (r)

$r = \frac{T_2}{T_1}$

$r = \frac{6}{2}$

$r = 3$

The 15th term is calculated as thus:

$T_n = ar^{n-1}$

Where

$a = 2$ and $n = 15$

$T_n = 2 * 3^{15-1}$

$T_n = 2 * 3^{14}$

$T_{15} = 2 * 4782969$

$T_{15} = 9565938$

The 15th term is 9,565,938