Question

Is 5, 10, 20, 40, 80, 160 a geometric sequence?

Answer 1

Yes it is.

Explanation:

To see if a sequence is geometric you have to check if every term (except the first) can be calculated by multiplying the previous term by the same constant.

In this case it is true. All terms are formed by multiplying previous one by `2`

The sequence can be written as:

`5;5color(red)(*2)=10;10color(red)(*2)=20; 20color(red)(*2)=40;...`

Answer 2

`r = 40/20 = 20/10 = 10/5 = 2`

Yes, geometric!

Explanation:

In a geometric sequence, each term is multiplied by the same number to get to the next term. This number is called the common ratio and is denoted by `r`

To check whether a sequence is geometric, find `r`, the quotient between any two consecutive terms, (divide them).

If `r` is always the same, it is geometric.

`r = T_4/T_3 =T_3/T_2 = T_2/T_1`

In general terms, `r` is found by dividing a term by the preceding term,
`r = T_n/T_(n-1)`

In this case, `40/20 = 2, and 20/10 = 2, and 10/5 = 2`

Yes, geometric! with `r=2`