a) Write five consecutive even and odd integers of -555.
Answers
Answer:
even and odd number concept is with the whole numbers not the negative integers. so there are 0 or no consecutive even and odd integers of -555.
Step-by-step explanation:
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Answer:
Take
x
. This is the smallest integer. Since these are consecutive odd integers, the second must be
2
greater than the first. The third number must be
2
greater than the second. And so forth.
For example,
1
,
3
,
5
,
7
,
and
9
are five consecutive odd integers, and they are all two more than the last. So, our five numbers are
x
,
x
+
2
,
(
x
+
2
)
+
2
,
(
(
x
+
2
)
+
2
)
+
2
,
and
(
(
(
x
+
2
)
+
2
)
+
2
)
+
2
which means
x
,
x
+
2
,
x
+
4
,
x
+
6
,
and
x
+
8
According to the question, their average is
−
21
. So,
x
+
(
x
+
2
)
+
(
x
+
4
)
+
(
x
+
6
)
+
(
x
+
8
)
5
=
−
21
Therefore, by simplifying,
5
x
+
20
5
=
−
21
So
5
x
+
20
=
−
105
Then
5
x
=
−
125
and
x
=
−
25
Shortcut: Since these are odd integers that are consecutive, you can take
−
21
as the middle number,
−
23
as the second,
−
19
to even out the
−
23
and maintain the average of
−
21
, then
−
25
as the first, then
−
17
as the last. This is a little hard to explain but makes sense if you really think about it.