Transmission Tower puzzle

The subject of this article is from the initial release.
The information from this article is up-to-date as of 25 November, 2016.

Transmission Tower puzzles are a game mechanic.

An example of Puzzle 3

Summary

See: Gek Observatory puzzle, Korvax Observatory puzzle, Vy'keen Observatory puzzle

Transmission Towers contain an interactive terminal that provides the player with a numerical puzzle to solve, along with some (random) flavor text.

The Options for solving a puzzle are randomly sorted, but in this article the correct solution will always be the first entry, and will be Bolded.

The puzzles are sorted in order of the first number in the puzzle sequence.

Puzzle 1

This puzzle is the Fibonacci sequence starting from 1,3 :
1 + 3 = 4
1 - 3 - 4 - 7 -11 - 18 - XX

1. 29
2. 28
3. 27

Puzzle 2

This puzzle is two interleaved sequences:
a_n+1 = _n + 2 with a₁ = 1 :
a_n+1 = _n + 2 with a₁ = 5 :
The next term will be the next term of the first sequence, which is 7.
1, 3, 5, 7
5, 7, 9,
1 - 5 - 3 - 7 - 5 - 9 - X

1. 7
2. 8
3. 6

Puzzle 3

This puzzle is the sequence of factorials multiplied by two, a_n = 2 * n! :
*2, *3, *4, *5, *6
2 - 4 - 12 - 48 - 240 - XXX

1. 1440
2. 1240
3. 1540

Puzzle 4

This puzzle is the sequence of factorials, a_n = n! :
*2, *3, *4, *5, *6
1 - 2 - 6 - 24 - 120 - XXX

1. 720
2. 620
3. 180

Puzzle 5

This puzzle is the Fibonacci sequence starting from 3,5 :
3 + 5 = 8
3 - 5 - 8 - 13 - 21 - XX

1. 34
2. 32
3. 35

Puzzle 6

This puzzle is the sequence a_n+1 = 3 * a_n - 1 with a₁ = 5 :
5 * 3 - 1 = 14
5 - 14 - 41 - 122 - XXX

1. 365
2. 355
3. 356

Puzzle 7

This puzzle is the sequence a_n+1 = 2 * a_n - 1 with a₁ = 17 :
17 * 2 - 1 = 33
17 - 33 - 65 - 129 - XXX

1. 257
2. 258
3. 261

Puzzle 8

This puzzle is the sequence a_n+1 = 2 * a_n - 1 with a₁ = 23 :
23 * 2 - 1 = 45
23 - 45 - 89 - 177 - XXX

1. 353
2. 186
3. 392

Puzzle 9

This puzzle is the sequence a_n+1 = a_n + (2 + n) with a₁ = 56 :
+3, +4, +5, +6, +7
56 - 59 - 63 - 68 - 74 - XX

1. 81
2. 80
3. 83

Puzzle 10

This puzzle is the sequence a_n+1 = a_n - (9 + 1 - n) :
-9, -8, -7, -6
80 - 71 - 63 - 56 - XX

1. 50
2. 49
3. 48

Puzzle 11

This puzzle is the sequence a_n+1 = a_n - (7 + 1 - n) :
-7, -6, -5, -4
99 - 92 - 86 - 81 - XX

1. 77
2. 79
3. 95

Puzzle 12

This puzzle is the reverse sequence of factorials, a_n = (8 - n)! :
/7, /6, /5, /4
5040 - 720 - 120 - 24 - X

1. 6
2. 8
3. 12