There are 21 marbles in a blue jar. the blue jars has 3 times as many marbles as a red jar. let m be the number of marbles in the red jar

m=7

Step-by-step explanation:

1 blue jar = 21 marbles

1 blue jar = 3 red jars

Therefor

21 marbles= 3 red jars

(Now let m=1 red jar)

21= 3m

(Then sine we have 3m dived both sides by 3 to isolate the m)

21/3= 3m/3

7=m

, 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