Ortega is trying to fill three bags equally with sand. He wants the bags to weigh the same. If the bags currently weigh 55 pounds, 51 pounds, and 48 pounds. Can Ortega get each bag to weigh the same by moving the weight around?

  yes

Step-by-step explanation:

The average weight of the three bags is ...

  (55 +51 +48)/3 = 154/3 = 51 1/3 . . . pounds

By removing 3 2/3 pounds of sand from the heaviest bag, adding 1/3 pound to the middle-weight bag, and the remaining 3 1/3 pounds to the lightest bag, Ortega can make all of the bags weigh the same: 51 1/3 pounds.

step-by-step explanation:

, 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