Question

A jogger ran `1/3` mile on day 1, and `2/3` mile on day 2, and 1`1/3` miles on day 3, and 2`2/3` miles on day 4, and this pattern continued for 3 more days. What expression represents the total distance the jogger ran?

Answer 1

A.

Explanation:

`Sigma1/3(2)^(d-1)` is the only rule that seems to work, the seven on the top indicates the integer to which the sum must be carried out, starting at `d=1` using this rule.

This `Sigma1/3(2)^(d-1)` is the only answer choice that works for Day 1 even, as the jogger needs to have run `1/3` mile on day `1`:
`Sigma1/3(2)^(d-1)= 1/3(2)^(1-1)= 1/3(2)^(0)= 1/3(1)= 1/3` miles for day 1