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densk [106]
2 years ago
11

A pattern has 3 blue triangles to every 24

Mathematics
1 answer:
NARA [144]2 years ago
5 0

Answer:

<u>It</u><u> </u><u>is</u><u> </u><u>3</u><u> </u><u>:</u><u> </u><u>2</u><u>7</u>

Step-by-step explanation:

Ratio of blue to yellow = 3:24

{ \sf{total \: ratio = 24 + 3 = 27}}

ratio of blue to all triangles:

=  3 : 27

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2.295 seconds

Step-by-step explanation:

39.09-36.795

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What do they call a number that goes on forever?
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Write a rule for the nth term of the sequence.
Helga [31]

Answer:

The rule for given sequence is: a_n = -27+16n

And the 100th term is: 1573

Step-by-step explanation:

Given sequence is:

-11, 5, 21, 37, 53, ...

Here

a_1 = -11\\a_2 = 5\\a_3 = 21\\a_4 = 37

First of all, we have to find if this is an arithmetic sequence

For that purpose, the common difference has to be found. Common difference, denoted by d, is the difference between consecutive terms of an arithmetic sequence

So,

d = a_2 -a_1 = 5-(-11) = 5+11 = 16\\d = a_3 -a_2 = 21-5 = 16\\d = a_4-a_3 = 37-21 = 16

As the common difference is same, the sequence is an arithmetic sequence

General rule for arithmetic sequence is:

a_n = a_1+(n-1)d

Putting values

a_n = -11+(n-1)(16)\\a_n = -11+16n-16\\a_n = -27+16n

For 100th term,

Putting n=100

a_{100} = -27+16(100)\\a_{100} = -27+1600 = 1573

Hence,

The rule for given sequence is: a_n = -27+16n

And the 100th term is: 1573

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