Question
Select all sequences that are geometric. (A) 1.5,6,24,96,ldots x (B) 2,4,6,8,10,ldots 25,5,1,(1)/(5),(1)/(25),ldots x (D) The circumference of a tree trunk grows 2.5 inches each year: 8.25,10.75,13.25,15.75,ldots (E) 1,-1.5,2.25,-3.375,ldots COMPLETE For each of the geometric sequences, determine the common ratio. Sequence A has common ratio 14 square COMPLETE Sequence C has common ratio square COMPLETE Sequence E has common ratio square square
Solution
3.3
(250 Votos)
Joana
Mestre · Tutor por 5 anos
Resposta
To determine if a sequence is geometric, we need to check if the ratio between consecutive terms is constant. Let's analyze each sequence:(A)
To find the common ratio, divide each term by the previous term:
,
,
The common ratio is 4, so this sequence is geometric.(B)
Divide each term by the previous term:
,
,
,
The ratios are not constant, so this sequence is not geometric.(C)
Divide each term by the previous term:
,
,
,
The common ratio is
, so this sequence is geometric.(D) The circumference of a tree trunk grows 2.5 inches each year:
Divide each term by the previous term:
,
,
The ratios are not constant, so this sequence is not geometric.(E)
Divide each term by the previous term:
,
,
The common ratio is -1.5, so this sequence is geometric.Now, let's determine the common ratios for the geometric sequences:Sequence A has a common ratio of 4.Sequence C has a common ratio of
.Sequence E has a common ratio of -1.5.