There are 85 telephones in the editorial department of glencoe publishing company. how many 2- way connections can be made among the office phones?

All of the telephones * all of the telephones minus one (because one is in use)

85 * 84 = 7140 connections

step-by-step explanation:

1

, 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