The local sandwich shop manager is slicing deli meat for lunch. He needs to slice the same amount of pepperoni as salami. He needs three times as many pounds of ham as he does pepperoni. He needs twice as much turkey as he needs ham. If the manager slices 44 pounds of deli meat, complete the table to determine the number of pounds of pepperoni and the number of pounds of turkey he slices.

, 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

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