Question 7

Explanation

Yanuar's running training pattern forms a geometric sequence because the distance doubles every week. This means the common ratio ($r$) of the sequence is $2$.

The key information we have is the distance in the $3\text{rd}$ week ($U_3$), which is $4\text{ km}$. Using the formula for the $n\text{-th}$ term of a geometric sequence, $U_n = ar^{n-1}$, we can backtrack to find the initial distance in the first week ($a$):

Now that we know Yanuar started by running $1\text{ km}$ in the first week, we can calculate the total distance over $5$ weeks ($S_5$) using the geometric series sum formula $S_n = \frac{a(r^n - 1)}{r - 1}$:

Thus, the total distance covered by Yanuar during the training is $31\text{ km}$.