Jill and Gary share £63 in the ratio 2:5
Work out how much each person gets.

Jill gets €18 Gary gets €45.

Step-by-step explanation:

First you add the two numbers of the ratio together. 2+5=7. Then you divide the constant, 63, by the total of the ratio, 7. 63/7=9. Then you multiply each number of the ratio by the quotient. 2 x 9= 18. 5 x 9= 45.

, 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

thats not a system of equations, that is a solution