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andrew11 [14]
2 years ago
15

"Which of the following sequences of numbers are arithmetic sequences? Check all that apply.

Mathematics
2 answers:
defon2 years ago
5 0
B) 154, 171, 188, 205, 222
A constant value (17) is added to get the next number
klasskru [66]2 years ago
3 0

Answer:

Option B, C, D

Step-by-step explanation:

We have to find the arithmetic sequence from the sequences given in the question.

To solve this question we will use the property of an arithmetic sequence that every successive term of an arithmetic sequence has a common difference.

(A) 1, -2, 3, -4, 5 .....

d_{2}-d_{1} = -2 -1 = -3

d_{3}-d_{2} = 3 - (-2) = 3 + 2 = 5

Sequence is not an arithmetic sequence

(B)  154, 171, 188, 205, 222 .....

a_{2}-a_{1} = 171- 154 = 17

a_{3}-a_{2} = 188 - 171 = 17

The sequence is an arithmetic sequence having common difference = 17

(C) 12,345, 12,346, 12,347......

a_{2}-a_{1} = 12,346 - 12,345 = 1

a_{3}-a_{2} = 12,347 - 12,346 = 1

Therefore, the sequence is an arithmetic sequence

(D) -3, -10, -17, --24, -31

a_{2}-a_{1} = -10 + 3 = ( -7 )

a_{3}-a_{2} = -17 + 10 = ( -7 )

This sequence is an arithmetic sequence

(E) 1, 8, 16, 24, 32 ....

a_{2}-a_{1} = 8 - 1 = 7

a_{3}-a_{2} = 16 - 8 = 8

Difference in terms is not common. Therefore, sequence is not an arithmetic sequence.

Option B,C,D are arithmetic sequences.

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2 years ago
Arrange the fractions in increasing order 7/15, 2/3, 11/12, 5/9
RoseWind [281]
To compare fraction sizes, you have to make sure the denominators of the fractions are the same. You must find a number that is a multiple of all the denominators we currently have (15, 3, 12, 9)
The smallest number that fits this is 540
Now you must multiply the numerator and denominator of each fraction by the number that makes the denominator 540
So, for 7/15 , we multiply the top and bottom by 36, since you need to multiply 15 by 36 to get 540. This means the fraction you end up with is 252/540
For 2/3, we multiply the top and bottom by 180, since you need to multiply 3 by 180 to get 540.This means the fraction you end up with is 360/540
For 11/12, we multiply the top and bottom by 45, since you need to multiply 12 by 45 to get 540. This means that the fraction you end up with is 495/540
For 5/9, we must multiply the top and bottom by 60, since you need to multiply 9 by 60 to get 540. This means that the fraction you end up with is 300/540

Now that the hard part is out of the way, you have four fractions: 252/540, 360/540, 495/540 and 300/540. Now, you can arrange the fractions in ascending order just based on their numerator. 
So, the order would be: 252/540, 300/540, 360/540, 495/540

Now, for the final step, just convert them back to the original fractions.
So, the final answer is:
7/15, 5/9, 2/3, 11/12

Hope I helped!! xx

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3 years ago
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PLEASE HELP ME QUICK!!
goldenfox [79]
Supplementary= 180 degrees

It took me a minute- but all you needed to find was half of 180 then divide that by two to get the answer.

180/2= 90

90/2= 45

Angle A= 45(3)= 135

Angle B= 45

135+45= 180

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