For each sequence, decide whether it could be arithmetic, a)  25,  5,  1,  ... b)  25,  19,  13,  ... c)  4,  9,  16,  ... d)  50,  60,  70,  ... e)  frac{1}{2},  3,  18,  ...

Dillard 2020-11-22 Answered
For each sequence, decide whether it could be arithmetic,
a)25,5,1,...
b)25,19,13,...
c)4,9,16,...
d)50,60,70,...
e)12,3,18,...
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Expert Answer

Sadie Eaton
Answered 2020-11-23 Author has 104 answers
Step 1 Given:
a)25,5,1,...b)25,19,13,...c)4,9,16,...d)50,60,70,...e)12,3,18,...
Step 2 Concept:
Let, the series a1,a2,a3,...
When
d=a2a1
d=a3a2
Then, the series is known as Arithmetic Series and d is called the common difference
When
r=a2a1
r=a3a2
Then, the series is known as the Geometric Series and r is called the common ratio
Part a
25,5,1,...
Here, r=a2a1=255=5
r=a3a2=51=5
This series is a Geometric Series with a common ratio of 5
Part b
25,19,13,...
Here, d=a2a1=1925=6
d=a3a2=1319=6
This series is Arithmetic Series with common difference –6
Part c
4,9,16,...
Here, d=a2a1=94=5
d=a3a2=169=7
This series is not Arithmetic Series because the common difference is not the same
Continuation from the last step:
4,9,16,...
Here, r=a2a1=94
r=(a3)/(a2)=169
This series is not Geometric Series because the common ratio is not the same
Part d
50,60,70,...
Here, d=a2a1=6050=10
d=a3a2=7060=10
This series is Arithmetic Series with a common difference of 10
Part e
12,3,18,...
Here, r=a2a1=312=6
r=a3a2=183=6
This series is a Geometric Series with a common ratio of 6

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