Is 48, 72, 108, 162 a sequence of arithmetic or geometric? Justify answer

Question

This is an Alegbra 2 question

Answer 1

Find the difference of consecutive terms as well as the ratio of consecutive terms  ...if their difference is same these will be arithmetic sequence and if their ratios are same this will be a geometric sequence.

 

 

T1=48,    T2= 72,     T3=108,      T4=162 

 

T2-T1= 72-48   = 24

T3-T2= 108-72 = 36 

T4-T3= 162-108 = 54

Difference of consecutive terms are not equal,therefore this will not be an arithmetic sequence.

 

T2/T1 = 72/48  =  3/2

T3/T2 = 108/72 = 3/2

T4/T3 = 162/108 = 3/2

 

Ratio of consecutive terms are equal ,therefore this will be definitely a geometric sequence..

Answer 2

72/48 = 3/2

 

108/72 = 3/2

 

162/108 = 3/2

 

The sequence is geometric with common ratio 3/2.