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

`T_(15) = 9565938`

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 = (T_2)/(T_1)`

`r = (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