A ladder of length 10 metres is leaning against a wall so that it is just touching a cube of edge length one metre. What height up the wall does the ladder reach?

24: 56

step-by-step explanation:

24 can be divided into 3 and 56 can be divided into 7, where as all the other ratios can't.

, 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

b

step-by-step explanation: