Question

How do you tell whether the sequence `100, 50, 25, 25/2, 25/4,...` is geometric?

Answer 1

The sequence is geometric with first term `a_1=100` and common ratio `r=0.5`

Explanation:

`a_1=100, a_2=50, a_3=25,a_4 = 25/2,a_5=25/4...`

`50/100=0.5 , 25/50=0.5 , (25/2)/25=0.5, (25/4)/(25/2)=0.5`

`:.a_2/a_1=a_3/a_2=a_4/a_3=a_5/a_4= 0.5`

The ratio of successive term and preceeding term is constant

`(r=0.5)` . Therefore the sequence is geometric whose first

term is `a_1=100` and common ratio is `r=0.5` [Ans]