Joanna Benson

2022-01-06

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

ambarakaq8

Expert

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

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