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

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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(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:
$$\displaystyle{27}+{4}={31}$$
$$\displaystyle{31}+{4}={35}$$
$$\displaystyle{35}+{4}={39}$$