6, 78, 85, 8, 17, 24, 10, 34

Obviously there is a pattern with term 1,4,7,10, 

6,         8,         10,

So we know that the pattern goes:

6, 78, 85, 8, 17, 24, 10, 34, __, 12, __, __, 14

So we need a pattern for

   78, 85,    17, 24,     34, __,     __, __,

We notice that 85-78=7 and also 24-17=7

So term 3,6,9,12,15,... are 7 more than the terms just before them

So the number after 34 must be 7 more than 34, which is 41

So we have the next term, where your ?? is.  Is that all you want?

6, 78, 85, 8, 17, 24, 10, 34, 41

Or do you need to go further?  If so you'd need a pattern for

   78,        17,         34,        __,   

So the pattern is:

Terms 1,4,7,10,13 go 6,8,10,12,14,16,...

Terms 2,5,8,11,14 go 78,17,34,129,

which has the pattern:

1. Multiply the number of term by 13
2. Subtract 152.
3. Multiply by the number of term.
4. Divide by 3
5. Add 162

We get that the 2nd term is 78 by
1. Multiplying 2 by 13, getting 26
2. Subtracting 152, getting -126
3. Multiplying by 2, getting -252
4. Dividing by 3, getting -84
5. Adding 162, getting 78, the 2nd term

We get that the 5th term is 17 by
1. Multiplying 5 by 13, getting 65
2. Subtracting 152, getting -87
3. Multiplying by 5, getting -435
4. Dividing by 3, getting -145
5. Adding 162, getting 17, the 5th term

We get that the 8th term is 34 by
1. Multiplying 8 by 13, getting 104
2. Subtracting 152, getting -48
3. Multiplying by 8, getting -384
4. Dividing by 3, getting -128
5. Adding 162, getting 34, the 8th term   
  
It's complicated, but it works.

Edwin