This is not a G.P., however we can relate it to a G.P. by writing the terms as Sn = 8 +88 + 888 + 8888 + ...... to n terms
Now, Sn =

8

9

[9 + 99 + 999 ...... to n terms]
=

8

9

[(10 - 1) + (100 - 1) + (1000 - 1) + ... to n terms]
=

8

9

[(10 + 100 + 1000 + ... to n terms) - (1 + 1 + ... to n temrs)]
=

8

9

[(10 + 102+103 + ... to n terms) - (1 + 1 + 1 + ... to n terms)]
=

8

9

[

10(10n−1)

9

−n]
Since Sn = a

(rn−1)

r−1

, if |r| > 1.