Identify the sequences as arithmetic or geometric. a. 2, 6, 18,

Joanna Benson 2022-01-06 Answered
Identify the sequences as arithmetic or geometric.
a. 2, 6, 18, 54, 162
b. 1, 8 ,15, 22, 29
c. 11, 15, 19, 23, 27

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Expert Answer

ambarakaq8
Answered 2022-01-07 Author has 1239 answers

(a) Given sequence is \(\displaystyle{2},{6},{18},{54},{162}\)
Ratio of two consecutive terms is constant. Therefore, sequence is geometric and common ratio is \(\displaystyle{r}=\frac{{6}}{{2}}\), that is \(\displaystyle{r}={3}\)
Next term can be obtained by multiplying the previous term by r. Therefore, next three terms are
\(\displaystyle{162}\times{3}={486}\)
\(\displaystyle{486}\times{3}={1458}\)
\(\displaystyle{1458}\times{3}={4374}\)
(b) Given sequence is \(\displaystyle{1},{8},{15},{22},{29}\)
Difference of two consecutive terms is constant. Therefore, sequence is arithmetic and common difference is \(\displaystyle{d}={8}-{1}={7}\),
Next term can be obtained by adding the previous term by d. Therefore, next three terms are:
\(\displaystyle{29}+{7}={36}\)
\(\displaystyle{36}+{7}={43}\)
\(\displaystyle{43}+{7}={50}\)
(c) Given sequence is \(\displaystyle{11},{15},{19},{23},{27}\)
Difference of two consecutive terms is constant. thus, sequence is arithmetic and common difference is \(d=15-11=4.\)
Next term can be obtained by adding the previous term by d. Therefore, next three terms are:
\(\displaystyle{27}+{4}={31}\)
\(\displaystyle{31}+{4}={35}\)
\(\displaystyle{35}+{4}={39}\)

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