A mixture of orange paint contains 8 teaspoons of red paint and 12 teaspoons of yellow paint. To make the same shade of orange paint using 18 teaspoons of red paint, how much yellow paint would you need?

27 spoons of yellow paint

Step-by-step explanation:

Red paint : Yellow paint = 8 : 12

Let 'x' be the number of spoons of yellow paint.

8 : 12 :: 18 : x

Product of extremes = Product of means

8 * x = 12 * 18

     x = 3 *9

     x = 27 spoons

, 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