Harrison is playing a board game that has a path of 100 spaces. after his first turn, he is 1/5 of the way along the spaces. on his second turn, he moves 1/4 fewer spaces than he moves on his first turn. on his third turn, he moves 1 1/4 times as many spaces than he moves on his first turn. what space is he on after all three turns?

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for

jwjeh; hw; kjhekjhkjhwkejhkw

step-by-step explanation: