Three consecutive even numbers have a sum where one half of that sum is between 90 and 105. write an inequality to find the the three numbers. let n represents the smallest even number. solve the inequality

90 <  [( n + n + 2 + n + 4) / 2] < 105

90 <  (3n + 6) / 2 < 105

3n + 6 > 180      and       3n + 6 <  210

n > 58     ,     n <  68

58  < n < 68   answer

, 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