No. A geometric progression (u_n) with ratio r and first term a satisfies:

For every n, u_n = a × r^n.

Ratio r and first term a are fixed, exponent n varies. The sequence (u_n) does grow (or decrease) exponentially fast.

At least that’s what the English definition is, and in my first language as well. If there is one in which “geometric” means “power function”, I’d actually be curious to know.