SOLUTION: sum of the numbers of the series: 6+9+21+69+261+........upto n terms

For k = 1, a1 =   6 =   1+5 = 4^0+5 
For k = 2, a2 =   9 =   4+5 = 4^1+5
For k = 3, a3 =  21 =  16+5 = 4^2+5
For k = 4, a4 =  69 =  64+5 = 4^3+5
For k = 5, a5 = 261 = 256+5 = 4^4+5
...
For k = n-1, an = 261 = 4^(n-1)+5

So we add the sequence 

with the geometric series formula to n terms:

 with a1 = 1
and r = 4.






 
Then we must add 5 to that n times which is the same as adding 5n

Answer:  

Edwin