Question

Consider the pattern below. 5+5/3+5/9+5/27+5/81+... What does this pattern represent? an arithmetic series an arithmetic sequence a geometric series a geometric sequence

Answer 1

Answer:

geometric series

Step-by-step explanation:

as all the terms are being added, so it is a series not a sequence. common ratio between all the terms as 1/3, if commo ratio comes out to be same after dividing 2nd term with first term or dividing third term with secoond term and so o , then the series or sequence is geometric. As terms are added and ratio between two consecutive terms is same for all i.e 1/3, so given sequence is geometric series.

it would be arithmetic series if common difference between two terms would be same.

Answer 2

Answer: choice C) geometric series

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Explanation:

The sequence {5, 5/3, 5/9, 5/27, 5/81, ...} is a geometric sequence with starting term a = 5 and common ratio r = 1/3

A geometric sequence is such that each term is generated by multiplying the last term by the same common ratio to get the next term

• first term = a = 5
• second term = (first term)*(common ratio) = a*r = 5*(1/3) = 5/3
• third term = (second term)*(common ratio) = (5/3)*(1/3) = 5/9
• fourth term = (third term)*(common ratio) = (5/9)*(1/3) = 5/27
• fifth term = (fourth term)*(common ratio) = (5/27)*(1/3) = 5/81

and so on. When we add up terms in a sequence, we form a series.