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, ...

Question

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,  ...

Sadie Eaton · Accepted Answer

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=a2−a1  d=a3−a2  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=a2−a1=19−25=−6   d=a3−a2=13−19=−6  This series is Arithmetic Series with common difference –6  Part c  4,  9,  16,  ...  Here, d=a2−a1=9−4=5   d=a3−a2=16−9=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=a2−a1=60−50=10   d=a3−a2=70−60=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

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, ...

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