We start with the given sequence of an increasing geometric progression (G.P.). Two key conditions are provided:

Calculating using given conditions:

Using the sequence terms:

Then:

27 2 It follows:

… ..(i)

Using the second condition:

Substituting :

Solving for and :
From equation (i) and (ii), we derive :

Since the G.P. is increasing, .
Solve for :
Substituting into :

Calculating the requested sum:
The task is to find:

Substitute the values:

Therefore, the value is 129.

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