X is a discrete random variable with a geometric distribution, $X \sim Geo(0.4)$, counting the number of trials up to and including the first success.

The probability of success on any one trial is $p = 0.4$, so the probability of failure is $q = 0.6$.

X exceeds 7 exactly when the first seven trials all fail, so $P(X > 7) = 0.6^{7} = 0.0279936$.

Therefore $P(X \le 7) = 1 - 0.0279936 = 0.9720064$, which is 0.972 to 3 significant figures and 0.97 to 2 significant figures.

Working through the tail is much quicker than adding the seven separate terms $0.4, 0.4(0.6), 0.4(0.6)^{2}, \dots$, though that sum gives the same value.