Hello everyone!

Here is the next question.

## Question of the Day - 40 points

Complete at least 3 of the 4 questions correctly to get 40 points.

Getting all 4 questions will give you an achievement package! The last one is pretty difficult.

Find the next three terms of the following sequences.

1. 3, 7, 13, 19, 29, 37.... 2. 1, -4, 27, -256, 3125.... 3. 0, 2, 6, 12, 20, 30, 42.... 4. 1, 1, 1, 3, 2, 6, 3, 10, 5, 15, 8, 21, 13....

## Previous Solution

The previous answer was 5/72 and (3,1,3; 1,1,6).

1) (quoted from 3primetime3, substituted *k* to *t* for consistency, sorry!)

- Having two "3 points" in three throws in any order means that the following results can happen in three specific orders: 3, 3, t; 3, t, 3; and t, 3, 3 (where t is a number from 1-6 inclusive except for 3).

Adding up the probabilities, (1/6*1/6*5/6) or (1/6*5/6*1/6) or (5/6*1/6*1/6)=5/216+5/216+5/216 = 15/216.

2) (quoted from Imamadmad, *t* for Tom and *k* for Kevin.)

- So Tom rolls a score of 3+
*t*+3>6. Tom's second throw is small, so he rolls (3,t,3).

Kevin rolls the following: (1,1,k), which is a score of 1+1+*k*>3+*t*+3>6

- Simplify: 2+
*k*>6+*t*>6 =*k*>4+*t*>4

- Since the dice has only 6 sides,
*k*< or =6

- Therefore,
*k*=6 and*t*=1

- Therefore, Tom's rolls: 3, 1, 3 and Kevin roles: 1, 1, 6

## Scoreboards

1. Blueeighthnote: 1265 points (2 achvmt pkgs)

2. TimBluesWin: 625 points (1 achvmt pkg)

3. Imamadmad: 180 points (1 achvmt pkg)

4. Julianthewiki: 100 points (1 achvmt pkg)

5. 69.235...:35 points (1 achvmt pkg)

6. Zombiebird4000: 20 points (1 achvmt pkg)

7. Supermario3459: 15 points (1 achvmt pkg)

8. Wildoneshelper: 10 points (1 achvmt pkg)