Consecutive Integers

Number Theory Level pending

Two sets $\{a_n\}$ and $\{b_n\}$ of 4 consecutive positive integers have exactly one integer in common. Let

$A$ denote the sum of the integers in $\{a_n\}$ , which is the set with the greater numbers, and
$B$ denote the sum of the integers in $\{b_n\}$ .

Find $A-B$ .

24 12 8 it can not be detemined 20

1 solution

Hana Wehbi
Jun 22, 2016

We can write $A \ and \ B$ as follows:

$B :\{ n + (n+1) + (n+2) + (n+3)\}$ and

$A: \{(n+3) + (n+4) + (n+5) + (n+6)\}$ for $n>0$ .

Note that each term in the second set is $3$ more than the equivalent term in the first set. Since there are four terms, then the total differences will be $4 \times 3 = 12$

Consecutive Integers

1 solution

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