Identify the sequences as arithmetic or geometric. a. 2, 6, 18, 54, 162 b. 1,...

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