mav24
21.02.2021 •
Mathematics
Use differences to find a pattern in the sequence.
7, 17, 30, 51, 85, 137, 212
Assuming that the pattern continues, the eighth term should be
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Ответ:
451
Step-by-step explanation:
7, 17, 30, 51, 85, 137, 212
Differences between Difference between Difference between
numbers in sequence first differences second differences
17 - 7 = 10
30 - 17 = 13 3
51 - 30 = 21 8 5
85 - 51 = 34 13 5
137 - 85 = 52 18 5
212 - 137 = 75 23 5
75 + 28 = 103
212 + 103 = 315 28 5
103 + 33 = 136
315 + 136 = 451 33 5
Ответ:
Well, just remember that the total is
180
∘
for any triangle, ever. So, what we can construct are some simple relationships:
∠
A
=
∠
A
(1)
2
∠
B
=
∠
A
→
∠
B
=
∠
A
2
(2)
∠
C
=
∠
B
2
−
2
∘
→
∠
C
=
∠
A
4
−
2
∘
(3)
So, we can add them up to write and determine
∠
A
(and thus the other two):
∠
A
+
∠
B
+
∠
C
=
180
∘
∠
A
+
∠
A
2
+
∠
A
4
−
2
∘
=
180
∘
∠
A
+
∠
A
2
+
∠
A
4
=
182
∘
4
∠
A
4
+
2
∠
A
4
+
∠
A
4
=
182
∘
4
∠
A
+
2
∠
A
+
∠
A
=
728
∘
7
∠
A
=
728
∘
∠
A
=
104
∘
And of course, just plug things back into (2) and (3) to finish things up.
∠
B
=
52
∘
∠
C
=
24
∘
We can then verify that we've matched the conditions given.
∠
A
is indeed twice
∠
B
.
∠
C
is indeed
2
∘
less than half of
∠
B
. Finally, you can easily convince yourself that the three angles add up to
180
∘
.