Let's call n the number of days Marika's been training for the race, and [tex] a_n [/tex] the distance she runs on the nth day in meters. After the first day, when n = 1, she runs 100 meters, so
[tex] a_1=100 [/tex]
On the second day, she runs an additional 4 meters, on the third day, another 4, and so on. Here's what that looks like mathematically:
[tex] a_2=100 + 4\\a_3=100 + 4 + 4\\a_4=100+4+4+4 [/tex]
It would be easier to write this continued addition as multiplication, in which case those same equations would look like
[tex] a_2 = 100 + 4(1)\\a_3 = 100 + 4(2)\\a_4=100+4(3) [/tex]
Notice that, in every case, the number 4 is being multiplied by is 1 less than n. We could even write for our first term that [tex] a_1=100+4(0) [/tex]. In general, we can say that
[tex] a_n=100+4(n-1) [/tex]
Which is expressed by option B.
(Bonus: What piece of information from this question did we not need to use here?)
